From e2fe7b25c78d9299dbb4149a588b361afed50635 Mon Sep 17 00:00:00 2001
From: harshkanhat <kanhatharsh@gmail.com>
Date: Wed, 28 Oct 2026 17:58:58 +0530
Subject: [PATCH 1/3] Fix binomial distribution overflow

---
 maths/binomial_distribution.py      | 7 ++-----
 maths/test_binomial_distribution.py | 8 ++++++++
 2 files changed, 10 insertions(+), 5 deletions(-)
 create mode 100644 maths/test_binomial_distribution.py

diff --git a/maths/binomial_distribution.py b/maths/binomial_distribution.py
index e29c8597a6e5..6b069461394e 100644
--- a/maths/binomial_distribution.py
+++ b/maths/binomial_distribution.py
@@ -1,8 +1,7 @@
 """For more information about the Binomial Distribution -
 https://en.wikipedia.org/wiki/Binomial_distribution"""
 
-from math import factorial
-
+from math import comb 
 
 def binomial_distribution(successes: int, trials: int, prob: float) -> float:
     """
@@ -26,9 +25,7 @@ def binomial_distribution(successes: int, trials: int, prob: float) -> float:
     if not 0 < prob < 1:
         raise ValueError("prob has to be in range of 1 - 0")
     probability = (prob**successes) * ((1 - prob) ** (trials - successes))
-    # Calculate the binomial coefficient: n! / k!(n-k)!
-    coefficient = float(factorial(trials))
-    coefficient /= factorial(successes) * factorial(trials - successes)
+    coefficient = comb(trials, successes)
     return probability * coefficient
 
 
diff --git a/maths/test_binomial_distribution.py b/maths/test_binomial_distribution.py
new file mode 100644
index 000000000000..4330c4286fce
--- /dev/null
+++ b/maths/test_binomial_distribution.py
@@ -0,0 +1,8 @@
+
+import pytest
+from maths.binomial_distribution import binomial_distribution
+
+def test_large_number_of_trials() -> None:
+    assert binomial_distribution(85, 171, 0.5) == pytest.approx(
+        0.060749764626165485
+    )

From fc834c5e32db6a46eb81b688ed583bbc9f432e06 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Wed, 28 Oct 2026 13:10:18 +0000
Subject: [PATCH 2/3] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 maths/binomial_distribution.py      | 3 ++-
 maths/test_binomial_distribution.py | 6 ++----
 2 files changed, 4 insertions(+), 5 deletions(-)

diff --git a/maths/binomial_distribution.py b/maths/binomial_distribution.py
index 6b069461394e..54958c614312 100644
--- a/maths/binomial_distribution.py
+++ b/maths/binomial_distribution.py
@@ -1,7 +1,8 @@
 """For more information about the Binomial Distribution -
 https://en.wikipedia.org/wiki/Binomial_distribution"""
 
-from math import comb 
+from math import comb
+
 
 def binomial_distribution(successes: int, trials: int, prob: float) -> float:
     """
diff --git a/maths/test_binomial_distribution.py b/maths/test_binomial_distribution.py
index 4330c4286fce..435c719d4bd0 100644
--- a/maths/test_binomial_distribution.py
+++ b/maths/test_binomial_distribution.py
@@ -1,8 +1,6 @@
-
 import pytest
 from maths.binomial_distribution import binomial_distribution
 
+
 def test_large_number_of_trials() -> None:
-    assert binomial_distribution(85, 171, 0.5) == pytest.approx(
-        0.060749764626165485
-    )
+    assert binomial_distribution(85, 171, 0.5) == pytest.approx(0.060749764626165485)

From 713f06021f83819164405b35bbc9800fcf97b370 Mon Sep 17 00:00:00 2001
From: harshkanhat <kanhatharsh@gmail.com>
Date: Wed, 28 Oct 2026 18:45:17 +0530
Subject: [PATCH 3/3] Fix import formatting in binomial distribution test

---
 maths/test_binomial_distribution.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/maths/test_binomial_distribution.py b/maths/test_binomial_distribution.py
index 435c719d4bd0..15ed043d731f 100644
--- a/maths/test_binomial_distribution.py
+++ b/maths/test_binomial_distribution.py
@@ -1,4 +1,5 @@
 import pytest
+
 from maths.binomial_distribution import binomial_distribution