diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index dcd16fc..930d22e 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -12,6 +12,7 @@ on:
       - "examples/**"
       - "LuaSF.lua"
       - "LuaStat.lua"
+      - "rockspec/**"
       - "*.rockspec"
       - ".github/workflows/ci.yml"
 
@@ -58,6 +59,7 @@ jobs:
           lua spec/test_sampling.lua
           lua spec/test_bivariate.lua
           lua spec/test_shape.lua
+          lua spec/test_probability.lua
 
       - name: Run examples
         run: |
@@ -70,4 +72,5 @@ jobs:
           lua examples/binomial_coin_flips.lua
           lua examples/bootstrap_mean.lua
           lua examples/covariance_correlation.lua
-          lua examples/skewness_kurtosis.lua
\ No newline at end of file
+          lua examples/skewness_kurtosis.lua
+          lua examples/probability_helpers.lua
diff --git a/.github/workflows/publish-luarocks.yml b/.github/workflows/publish-luarocks.yml
index fa7cc25..8c03841 100644
--- a/.github/workflows/publish-luarocks.yml
+++ b/.github/workflows/publish-luarocks.yml
@@ -6,7 +6,7 @@ on:
       rockspec:
         description: "Rockspec file to validate or publish"
         required: true
-        default: "rockspec/luasf-0.6.0-1.rockspec"
+        default: "rockspec/luasf-0.7.0-1.rockspec"
         type: string
       publish:
         description: "Publish to LuaRocks after validation"
@@ -50,6 +50,9 @@ jobs:
       - name: Test shape statistics entry point
         run: lua -e 'local stats = require("luasf"); print(stats.skewness({1,2,3,4,5})); print(stats.kurtosis({1,2,3,4,5}))'
 
+      - name: Test probability helpers entry point
+        run: lua -e 'local stats = require("luasf"); print(stats.factorial(5)); print(stats.combinations(5,2)); print(stats.permutations_with_repetition(10,4))'
+
       - name: Test LuaSF compatibility entry point
         run: lua -e 'local stats = require("LuaSF"); print(stats.sumF({1,2,3}))'
 
diff --git a/CHANGELOG.md b/CHANGELOG.md
index e6d414f..0a1a800 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -10,15 +10,52 @@ This project follows a lightweight changelog format inspired by [Keep a Changelo
 
 ### Planned
 
-* Continue improving examples and documentation.
 * Explore a lightweight cross-reference with LuaHMF as a related pure-Lua math helper project.
-* Evaluate future probability helpers such as `factorial`, `combinations`, and `permutations`.
+* Add more distribution and simulation examples.
 * Evaluate optional formula-based simple regression summaries while keeping ML workflows outside the current scope.
-* Add more distribution examples and simulation-oriented examples.
 
 ---
 
-## [0.6.0] - 2026-06-07
+## [0.7.0] - 2026-06-07
+
+### Added
+
+* Implemented `src/luasf/probability.lua` with probability and combinatorics helpers.
+* Added `factorial(n)`.
+* Added `permutations(n, r)` for ordered selections without repetition.
+* Added `combinations(n, r)` for unordered selections without repetition.
+* Added `permutations_with_repetition(n, r)` for ordered selections with repetition.
+* Added `combinations_with_repetition(n, r)` for unordered selections with repetition.
+* Added `permutations_without_repetition(n, r)` as an alias for `permutations(n, r)`.
+* Added `combinations_without_repetition(n, r)` as an alias for `combinations(n, r)`.
+* Added `nPr(n, r)` as an alias for `permutations(n, r)`.
+* Added `nCr(n, r)` as an alias for `combinations(n, r)`.
+* Added `multiset_permutations(counts)` for distinct arrangements of repeated item groups.
+* Added `spec/test_probability.lua`.
+* Added `examples/probability_helpers.lua`.
+* Added `rockspec/luasf-0.7.0-1.rockspec`.
+
+### Changed
+
+* Updated CI to run probability helper tests and the new probability example.
+* Updated the LuaRocks publishing workflow default rockspec path to `rockspec/luasf-0.7.0-1.rockspec`.
+* Updated README, API documentation, changelog, and contribution notes for probability helpers.
+
+### Notes
+
+Probability helpers distinguish common combinatorics cases:
+
+* Ordered selections without repetition: `permutations(n, r)` and `nPr(n, r)`.
+* Ordered selections with repetition: `permutations_with_repetition(n, r)`.
+* Unordered selections without repetition: `combinations(n, r)` and `nCr(n, r)`.
+* Unordered selections with repetition: `combinations_with_repetition(n, r)`.
+* Repeated item arrangements: `multiset_permutations(counts)`.
+
+Lua numbers may lose precision for very large combinatorial values. LuaSF intentionally keeps these helpers lightweight and dependency-free instead of adding big integer support.
+
+---
+
+## [0.6.0] - 2026-06-08
 
 ### Added
 
diff --git a/CONTRIBUTING.md b/CONTRIBUTING.md
index 0fbff42..04bf184 100644
--- a/CONTRIBUTING.md
+++ b/CONTRIBUTING.md
@@ -14,6 +14,7 @@ LuaSF aims to provide:
 * Summary statistics helpers
 * Shape statistics helpers such as skewness and kurtosis
 * Bivariate statistics helpers such as covariance and correlation
+* Probability and combinatorics helpers
 * Pseudo-random variable generation
 * Sampling utilities
 * A small and readable Lua codebase
@@ -153,6 +154,7 @@ lua spec/test_distributions.lua
 lua spec/test_sampling.lua
 lua spec/test_bivariate.lua
 lua spec/test_shape.lua
+lua spec/test_probability.lua
 ```
 
 Run examples:
@@ -168,10 +170,45 @@ lua examples/binomial_coin_flips.lua
 lua examples/bootstrap_mean.lua
 lua examples/covariance_correlation.lua
 lua examples/skewness_kurtosis.lua
+lua examples/probability_helpers.lua
 ```
 
 ---
 
+## Probability helper guidelines
+
+Probability and combinatorics helpers should live in:
+
+```text
+src/luasf/probability.lua
+```
+
+Tests should live in:
+
+```text
+spec/test_probability.lua
+```
+
+Examples should live in:
+
+```text
+examples/probability_helpers.lua
+```
+
+Probability and combinatorics helpers should remain lightweight and formula-based.
+
+For combinatorics helpers, please be explicit about whether order matters and whether repetition is allowed:
+
+* `permutations(n, r)` for ordered selections without repetition.
+* `combinations(n, r)` for unordered selections without repetition.
+* `permutations_with_repetition(n, r)` for ordered selections with repetition.
+* `combinations_with_repetition(n, r)` for unordered selections with repetition.
+* `multiset_permutations(counts)` for arrangements of repeated item groups.
+
+Please keep in mind that Lua numbers may lose precision for very large combinatorial values. LuaSF should remain dependency-free and should not add big integer libraries unless the project scope changes significantly.
+
+---
+
 ## LuaRocks packaging
 
 Rockspec files are kept under:
@@ -185,8 +222,8 @@ When adding new internal modules, update the next rockspec draft so LuaRocks kno
 Before publishing, validate locally or through GitHub Actions:
 
 ```bash
-luarocks lint rockspec/luasf-0.5.0-1.rockspec
-luarocks make rockspec/luasf-0.5.0-1.rockspec
+luarocks lint rockspec/luasf-0.7.0-1.rockspec
+luarocks make rockspec/luasf-0.7.0-1.rockspec
 ```
 
 Publishing should remain manual and intentional.
@@ -246,6 +283,9 @@ Before opening a pull request, please check:
 * New behavior includes at least one test.
 * New modules are included in the rockspec draft when needed.
 * Code remains readable and dependency-light.
+* LuaRocks rockspec files are updated when preparing a package release.
+* CI workflows are updated when new tests or examples are added.
+
 
 ---
 
@@ -258,6 +298,7 @@ Prefer:
 * Small functions
 * Minimal dependencies
 * Compatibility with Lua 5.1+
+* Explicit validation for public helpers
 * Formula-based helpers when appropriate
 
 Avoid:
@@ -272,12 +313,6 @@ Avoid:
 
 ## Future scope
 
-Potential future additions include:
-
-* `factorial(n)`
-* `combinations(n, r)`
-* `permutations(n, r)`
-
 Simple formula-based regression summaries may be considered later, but optimization-based models and ML workflows are outside the current scope.
 
 ---
diff --git a/README.md b/README.md
index 82d2be3..583db29 100644
--- a/README.md
+++ b/README.md
@@ -31,9 +31,9 @@
 
 **LuaSF** stands for **Lua Statistics Functions**.
 
-LuaSF is a small, lightweight, pure-Lua library for descriptive statistics, sampling utilities, and pseudo-random variable generation.
+LuaSF is a small, lightweight, pure-Lua library for descriptive statistics, shape statistics, bivariate statistics, probability helpers, sampling utilities, and pseudo-random variable generation.
 
-The project started around 2014 and was later published under the MIT License. It has now been revived with compatibility improvements, tests, examples, documentation, a cleaner module structure, additional statistics helpers, sampling utilities, and LuaRocks packaging while preserving the existing public API.
+The project started around 2014 and was later published under the MIT License. It has now been revived with compatibility improvements, tests, examples, documentation, a cleaner modular source structure, additional statistics helpers, sampling utilities, probability helpers, and LuaRocks packaging while preserving the existing public API.
 
 ---
 
@@ -47,6 +47,7 @@ The project started around 2014 and was later published under the MIT License. I
 * Basic descriptive statistics
 * Summary statistics helpers
 * Bivariate statistics helpers
+* Probability and combinatorics helpers
 * Sampling utilities
 * Discrete and continuous pseudo-random variables
 * Compatible with the existing public LuaSF API
@@ -111,6 +112,8 @@ print(stats.stddev(values))   -- sample standard deviation
 print(stats.median(values))   -- 3
 print(stats.variance(values)) -- sample variance
 print(stats.summary(values).count) -- 5
+print(stats.factorial(5))     -- 120
+print(stats.combinations(5, 2)) -- 10
 ```
 
 Legacy names are still available:
@@ -172,6 +175,23 @@ print(stats.stvF(values)) -- sample standard deviation
 | `correlation(x, y)` | Pearson correlation coefficient |
 | `pearson(x, y)` | Alias for `correlation(x, y)` |
 
+### Probability helpers
+
+| Function                                | Description                                                            |
+| --------------------------------------- | ---------------------------------------------------------------------- |
+| `factorial(n)`                          | Factorial of a non-negative integer                                    |
+| `permutations(n, r)`                    | Ordered selections without repetition, also known as `nPr`             |
+| `combinations(n, r)`                    | Unordered selections without repetition, also known as `nCr`           |
+| `permutations_with_repetition(n, r)`    | Ordered selections with repetition, calculated as `n^r`                |
+| `combinations_with_repetition(n, r)`    | Unordered selections with repetition, calculated as `C(n + r - 1, r)`  |
+| `permutations_without_repetition(n, r)` | Alias for `permutations(n, r)`                                         |
+| `combinations_without_repetition(n, r)` | Alias for `combinations(n, r)`                                         |
+| `multiset_permutations(counts)`         | Distinct arrangements of repeated item counts                          |
+| `nPr(n, r)`                             | Alias for `permutations(n, r)`                                         |
+| `nCr(n, r)`                             | Alias for `combinations(n, r)`                                         |
+
+> These helpers use Lua numbers. Very large inputs may exceed the practical numeric precision or range of the Lua runtime.
+
 ### Sampling utilities
 
 | Function                          | Description                                    |
@@ -341,6 +361,7 @@ LuaSF/
     test_sampling.lua
     test_bivariate.lua
     test_shape.lua
+    test_probability.lua
   examples/
     dice_simulation.lua
     normal_quality_control.lua
@@ -352,6 +373,7 @@ LuaSF/
     bootstrap_mean.lua
     covariance_correlation.lua
     skewness_kurtosis.lua
+    probability_helpers.lua
   docs/
     api.md
   .github/
@@ -364,6 +386,7 @@ LuaSF/
     luasf-0.4.0-1.rockspec
     luasf-0.5.0-1.rockspec
     luasf-0.6.0-1.rockspec
+    luasf-0.7.0-1.rockspec
   LuaSF.lua
   LuaStat.lua
   README.md
@@ -390,6 +413,7 @@ lua spec/test_stats.lua
 lua spec/test_distributions.lua
 lua spec/test_sampling.lua
 lua spec/test_bivariate.lua
+lua spec/test_probability.lua
 ```
 
 ---
@@ -406,6 +430,7 @@ lua examples/poisson_arrivals.lua
 lua examples/binomial_coin_flips.lua
 lua examples/bootstrap_mean.lua
 lua examples/covariance_correlation.lua
+lua examples/probability_helpers.lua
 ```
 
 ---
@@ -423,17 +448,18 @@ lua examples/covariance_correlation.lua
 * API documentation
 * Additional statistics helpers
 * Summary statistics helpers
+* Shape statistics helpers
 * Bivariate statistics helpers
+* Probability helpers
 * Sampling utilities
 * Deterministic simulation support
 * LuaRocks publishing
 
 ### Planned
 
-* More distribution and simulation examples
 * Lightweight cross-reference with LuaHMF
-* Future probability helpers such as `factorial`, `combinations`, and `permutations`
-* Optional formula-based simple regression summaries
+* More distribution and simulation examples
+* Optional simple formula-based regression summaries, without turning LuaSF into a machine learning framework
 
 ---
 
diff --git a/docs/api.md b/docs/api.md
index 44e6c40..fd9561c 100644
--- a/docs/api.md
+++ b/docs/api.md
@@ -435,6 +435,166 @@ stats.correlation(x, y)
 
 ---
 
+## Probability helpers
+
+Probability helpers are lightweight combinatorics utilities useful for counting cases in probability, simulation, teaching, and small scripts.
+
+LuaSF distinguishes helpers without repetition and with repetition where appropriate.
+
+> Lua numbers may lose precision for very large combinatorial values. LuaSF intentionally avoids big integer dependencies to remain small and pure Lua.
+
+### `factorial(n)`
+
+Returns the factorial of a non-negative integer.
+
+```lua
+local stats = require("luasf")
+
+print(stats.factorial(0)) -- 1
+print(stats.factorial(5)) -- 120
+```
+
+---
+
+### `permutations(n, r)`
+
+Returns the number of ordered selections of `r` elements from `n` distinct elements without repetition.
+
+This is commonly known as `nPr`.
+
+```text
+nPr = n! / (n - r)!
+```
+
+If `r` is omitted, LuaSF treats it as `n` and returns `n!`.
+
+```lua
+local stats = require("luasf")
+
+print(stats.permutations(5, 3)) -- 60
+print(stats.nPr(5, 3))          -- 60
+```
+
+Requirements:
+
+* `n` must be a non-negative integer.
+* `r` must be a non-negative integer.
+* `r <= n`.
+
+
+Alias:
+
+```lua
+stats.permutations_without_repetition(n, r)
+```
+
+---
+
+### `combinations(n, r)`
+
+Returns the number of unordered selections of `r` elements from `n` distinct elements without repetition.
+
+This is commonly known as `nCr`.
+
+```text
+nCr = n! / (r! * (n - r)!)
+```
+
+```lua
+local stats = require("luasf")
+
+print(stats.combinations(5, 3)) -- 10
+print(stats.nCr(5, 3))          -- 10
+```
+
+Requirements:
+
+* `n` must be a non-negative integer.
+* `r` must be a non-negative integer.
+* `r <= n`.
+
+
+Alias:
+
+```lua
+stats.combinations_without_repetition(n, r)
+```
+
+
+---
+
+### `permutations_with_repetition(n, r)`
+
+Returns the number of ordered selections of `r` elements from `n` possible values with repetition allowed.
+
+This is equivalent to:
+
+```text
+n^r
+```
+
+```lua
+local stats = require("luasf")
+
+print(stats.permutations_with_repetition(5, 3)) -- 125
+print(stats.permutations_with_repetition(10, 4)) -- 10000
+```
+
+Requirements:
+
+* `n` must be a non-negative integer.
+* `r` must be a non-negative integer.
+
+
+This is useful for cases such as PIN-like sequences, codes, or ordered choices where values can repeat.
+
+---
+
+### `combinations_with_repetition(n, r)`
+
+Returns the number of unordered selections of `r` elements from `n` possible values with repetition allowed.
+
+This is equivalent to:
+
+```text
+C(n + r - 1, r)
+```
+
+```lua
+local stats = require("luasf")
+
+print(stats.combinations_with_repetition(5, 3)) -- 35
+```
+
+Requirements:
+
+* `n` must be a positive integer.
+* `r` must be a non-negative integer.
+
+---
+
+### `multiset_permutations(counts)`
+
+Returns the number of distinct arrangements of repeated item groups.
+
+`counts` is an array containing how many times each repeated group appears.
+
+This is equivalent to:
+
+```text
+n! / (a! * b! * c! * ...)
+```
+
+where `n` is the sum of all counts.
+
+```lua
+local stats = require("luasf")
+
+print(stats.multiset_permutations({3, 2, 1})) -- 60
+```
+
+---
+
 ## Sampling utilities
 
 ### `choice(array)`
@@ -938,6 +1098,23 @@ stats.range
 stats.iqr
 stats.percentile
 stats.summary
+stats.central_moment
+stats.skewness
+stats.kurtosis
+stats.excess_kurtosis
+stats.covariance
+stats.correlation
+stats.pearson
+stats.factorial
+stats.permutations
+stats.combinations
+stats.permutations_with_repetition
+stats.combinations_with_repetition
+stats.permutations_without_repetition
+stats.combinations_without_repetition
+stats.multiset_permutations
+stats.nPr
+stats.nCr
 stats.choice
 stats.shuffle
 stats.sample
diff --git a/examples/probability_helpers.lua b/examples/probability_helpers.lua
new file mode 100644
index 0000000..5c0649f
--- /dev/null
+++ b/examples/probability_helpers.lua
@@ -0,0 +1,19 @@
+local stats = require("luasf")
+
+print("Probability helper examples")
+print("Factorial 5!:", stats.factorial(5))
+
+print("Ordered selections without repetition")
+print("Race podiums with 8 runners and 3 medals:", stats.permutations(8, 3))
+
+print("Ordered selections with repetition")
+print("4-digit PINs using digits 0-9:", stats.permutations_with_repetition(10, 4))
+
+print("Unordered selections without repetition")
+print("Committees of 3 people from 10 candidates:", stats.combinations(10, 3))
+
+print("Unordered selections with repetition")
+print("3 scoops from 5 ice cream flavors:", stats.combinations_with_repetition(5, 3))
+
+print("Distinct permutations of repeated items")
+print("Letters in MISSISSIPPI-style counts {4, 4, 2, 1}:", stats.multiset_permutations({4, 4, 2, 1}))
diff --git a/rockspec/luasf-0.7.0-1.rockspec b/rockspec/luasf-0.7.0-1.rockspec
new file mode 100644
index 0000000..33c9da9
--- /dev/null
+++ b/rockspec/luasf-0.7.0-1.rockspec
@@ -0,0 +1,41 @@
+package = "luasf"
+version = "0.7.0-1"
+
+source = {
+  url = "git://github.com/HubertRonald/LuaSF.git",
+  tag = "v0.7.0"
+}
+
+description = {
+  summary = "Lua Statistics Functions",
+  detailed = [[
+LuaSF is a lightweight, pure-Lua library for descriptive statistics,
+shape statistics, bivariate statistics, probability helpers, sampling utilities,
+simulation examples, and random variable generation.
+  ]],
+  homepage = "https://github.com/HubertRonald/LuaSF",
+  license = "MIT",
+  maintainer = "Hubert Ronald"
+}
+
+dependencies = {
+  "lua >= 5.1"
+}
+
+build = {
+  type = "builtin",
+  modules = {
+    luasf = "src/luasf.lua",
+    ["luasf.core"] = "src/luasf/core.lua",
+    ["luasf.validation"] = "src/luasf/validation.lua",
+    ["luasf.rng"] = "src/luasf/rng.lua",
+    ["luasf.descriptive"] = "src/luasf/descriptive.lua",
+    ["luasf.shape"] = "src/luasf/shape.lua",
+    ["luasf.sampling"] = "src/luasf/sampling.lua",
+    ["luasf.distributions"] = "src/luasf/distributions.lua",
+    ["luasf.bivariate"] = "src/luasf/bivariate.lua",
+    ["luasf.probability"] = "src/luasf/probability.lua",
+    LuaSF = "LuaSF.lua",
+    LuaStat = "LuaStat.lua"
+  }
+}
diff --git a/spec/test_probability.lua b/spec/test_probability.lua
new file mode 100644
index 0000000..7929b90
--- /dev/null
+++ b/spec/test_probability.lua
@@ -0,0 +1,135 @@
+local luaunit = require("luaunit")
+local stats = require("luasf")
+
+TestProbability = {}
+
+function TestProbability:test_factorial_zero()
+  luaunit.assertEquals(stats.factorial(0), 1)
+end
+
+function TestProbability:test_factorial_positive_integer()
+  luaunit.assertEquals(stats.factorial(5), 120)
+end
+
+function TestProbability:test_factorial_rejects_negative_values()
+  luaunit.assertError(function()
+    stats.factorial(-1)
+  end)
+end
+
+function TestProbability:test_factorial_rejects_non_integer_values()
+  luaunit.assertError(function()
+    stats.factorial(3.5)
+  end)
+end
+
+function TestProbability:test_permutations_requires_r_less_than_or_equal_to_n()
+  luaunit.assertError(function()
+    stats.permutations(3, 4)
+  end)
+end
+
+function TestProbability:test_combinations_requires_r_less_than_or_equal_to_n()
+  luaunit.assertError(function()
+    stats.combinations(3, 4)
+  end)
+end
+
+function TestProbability:test_combinations_with_repetition_requires_positive_n()
+  luaunit.assertError(function()
+    stats.combinations_with_repetition(0, 2)
+  end)
+end
+
+function TestProbability:test_permutations_without_repetition()
+  luaunit.assertEquals(stats.permutations(5, 2), 20)
+end
+
+function TestProbability:test_permutations_without_repetition_all_items()
+  luaunit.assertEquals(stats.permutations(5, 5), 120)
+end
+
+function TestProbability:test_combinations_without_repetition()
+  luaunit.assertEquals(stats.combinations(5, 2), 10)
+  luaunit.assertEquals(stats.combinations_without_repetition(5, 2), 10)
+  luaunit.assertEquals(stats.combinations(5, 0), 1)
+  luaunit.assertEquals(stats.combinations(5, 5), 1)
+end
+
+function TestProbability:test_permutations_without_repetition_zero_selected()
+  luaunit.assertEquals(stats.permutations(5, 0), 1)
+end
+
+function TestProbability:test_permutations_without_repetition_rejects_r_greater_than_n()
+  luaunit.assertError(function()
+    stats.permutations(3, 4)
+  end)
+end
+
+function TestProbability:test_combinations_without_repetition_symmetric_case()
+  luaunit.assertEquals(stats.combinations(10, 3), 120)
+  luaunit.assertEquals(stats.combinations(10, 7), 120)
+end
+
+function TestProbability:test_combinations_without_repetition_zero_selected()
+  luaunit.assertEquals(stats.combinations(5, 0), 1)
+end
+
+function TestProbability:test_combinations_without_repetition_all_items()
+  luaunit.assertEquals(stats.combinations(5, 5), 1)
+end
+
+function TestProbability:test_combinations_without_repetition_rejects_r_greater_than_n()
+  luaunit.assertError(function()
+    stats.combinations(3, 4)
+  end)
+end
+
+function TestProbability:test_permutations_with_repetition()
+  luaunit.assertEquals(stats.permutations_with_repetition(4, 3), 64)
+end
+
+function TestProbability:test_permutations_with_repetition_zero_selected()
+  luaunit.assertEquals(stats.permutations_with_repetition(4, 0), 1)
+end
+
+function TestProbability:test_permutations_with_repetition_empty_set_zero_selected()
+  luaunit.assertEquals(stats.permutations_with_repetition(0, 0), 1)
+end
+
+function TestProbability:test_permutations_with_repetition_empty_set_positive_selection()
+  luaunit.assertEquals(stats.permutations_with_repetition(0, 3), 0)
+end
+
+function TestProbability:test_combinations_with_repetition()
+  luaunit.assertEquals(stats.combinations_with_repetition(5, 3), 35)
+end
+
+function TestProbability:test_combinations_with_repetition_zero_selected()
+  luaunit.assertEquals(stats.combinations_with_repetition(4, 0), 1)
+end
+
+function TestProbability:test_combinations_with_repetition_single_item()
+  luaunit.assertEquals(stats.combinations_with_repetition(1, 5), 1)
+end
+
+function TestProbability:test_combinations_with_repetition_rejects_zero_items()
+  luaunit.assertError(function()
+    stats.combinations_with_repetition(0, 2)
+  end)
+end
+
+function TestProbability:test_multiset_permutations()
+  luaunit.assertEquals(stats.multiset_permutations({3, 2, 1}), 60)
+  luaunit.assertEquals(stats.multiset_permutations({2, 2}), 6)
+end
+
+function TestProbability:test_nPr_alias()
+  luaunit.assertEquals(stats.nPr(5, 2), 20)
+end
+
+function TestProbability:test_nCr_alias()
+  luaunit.assertEquals(stats.nCr(5, 2), 10)
+end
+
+os.exit(luaunit.LuaUnit.run())
diff --git a/src/luasf/probability.lua b/src/luasf/probability.lua
index 790f982..b86cf53 100644
--- a/src/luasf/probability.lua
+++ b/src/luasf/probability.lua
@@ -1,13 +1,110 @@
---[[
-Probability helpers placeholder.
+local module_name = ... or "luasf.probability"
+local prefix = module_name:match("^src%.") and "src.luasf." or "luasf."
 
-This module is intentionally small for now. Future versions may include
-factorial, combinations, permutations, and related probability helpers.
+local validation = require(prefix .. "validation")
 
-Those helpers should be added carefully to avoid overflow and to keep LuaSF
-focused on lightweight statistics, probability, and simulation utilities.
-]]
+local min = math.min
 
 local M = {}
 
+local function factorial(n)
+    validation.assert_non_negative_integer(n, "n")
+
+    local result = 1
+
+    for i = 2, n do
+      result = result * i
+    end
+
+    return result
+  end
+
+-- Ordered selections without repetition.
+-- Equivalent to nPr = n! / (n - r)!.
+-- If r is omitted, this returns n!.
+local function permutations(n, r)
+    validation.assert_non_negative_integer(n, "n")
+    r = r == nil and n or r
+    validation.assert_non_negative_integer(r, "r")
+    assert(r <= n, "r must be less than or equal to n")
+
+    local result = 1
+
+    for i = n - r + 1, n do
+      result = result * i
+    end
+
+    return result
+  end
+
+
+-- Ordered selections with repetition.
+-- Equivalent to n^r.
+local function permutations_with_repetition(n, r)
+    validation.assert_non_negative_integer(n, "n")
+    validation.assert_non_negative_integer(r, "r")
+
+    return n ^ r
+  end
+
+-- Unordered selections without repetition.
+-- Equivalent to nCr = n! / (r! * (n - r)!).
+local function combinations(n, r)
+    validation.assert_non_negative_integer(n, "n")
+    validation.assert_non_negative_integer(r, "r")
+    assert(r <= n, "r must be less than or equal to n")
+
+    r = min(r, n - r)
+
+    local result = 1
+
+    for i = 1, r do
+      result = result * (n - r + i) / i
+    end
+
+    return result
+  end
+
+-- Unordered selections with repetition.
+-- Equivalent to C(n + r - 1, r).
+local function combinations_with_repetition(n, r)
+    validation.assert_non_negative_integer(n, "n")
+    validation.assert_non_negative_integer(r, "r")
+    assert(n >= 1, "n must be greater than or equal to 1")
+
+    return combinations(n + r - 1, r)
+  end
+
+-- Distinct permutations of a multiset represented by repeated counts.
+-- Example: counts {3, 2, 1} -> 6! / (3! * 2! * 1!) = 60.
+local function multiset_permutations(counts)
+    validation.assert_non_empty_array(counts, "counts")
+
+    local total = 0
+    local denominator = 1
+
+    for _, count in ipairs(counts) do
+      validation.assert_non_negative_integer(count, "count")
+      total = total + count
+      denominator = denominator * factorial(count)
+    end
+
+    return factorial(total) / denominator
+  end
+
+  M.factorial = factorial
+  M.permutations = permutations -- without_repetition
+  M.combinations = combinations -- without_repetition
+  M.permutations_with_repetition = permutations_with_repetition
+  M.combinations_with_repetition = combinations_with_repetition
+  M.permutations_without_repetition = permutations
+  M.combinations_without_repetition = combinations
+  M.multiset_permutations = multiset_permutations
+
+  -- Common combinatorics aliases.
+  M.nPr = permutations
+  M.nCr = combinations
+
+
+
 return M
\ No newline at end of file
diff --git a/src/luasf/validation.lua b/src/luasf/validation.lua
index dcdbfa3..e2af90e 100644
--- a/src/luasf/validation.lua
+++ b/src/luasf/validation.lua
@@ -1,5 +1,7 @@
 local M = {}
 
+local floor = math.floor
+
 function M.assert_number(value, name)
   name = name or "value"
   assert(type(value) == "number", name .. " must be a number")
@@ -51,4 +53,20 @@ function M.assert_same_length_numeric_arrays(x, y, x_name, y_name)
   M.assert_numeric_array(y, y_name)
 end
 
+function M.assert_integer(value, name)
+  name = name or "value"
+  M.assert_number(value, name)
+  assert(value == floor(value), name .. " must be an integer")
+end
+
+function M.assert_non_negative_integer(value, name)
+  M.assert_integer(value, name)
+  assert(value >= 0, name .. " must be greater than or equal to 0")
+end
+
+function M.assert_positive_integer(value, name)
+  M.assert_integer(value, name)
+  assert(value >= 1, name .. " must be greater than or equal to 1")
+end
+
 return M
\ No newline at end of file