From 4f457c5786dab2e83f00d671e7721528ed385eb9 Mon Sep 17 00:00:00 2001
From: Naman-Vasudev <naman24vasudev@gmail.com>
Date: Mon, 20 Oct 2025 15:07:03 +0530
Subject: [PATCH 1/5] Create ncr_combinations.py

---
 maths/ncr_combinations.py | 74 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 74 insertions(+)
 create mode 100644 maths/ncr_combinations.py

diff --git a/maths/ncr_combinations.py b/maths/ncr_combinations.py
new file mode 100644
index 000000000000..ebe17735a32c
--- /dev/null
+++ b/maths/ncr_combinations.py
@@ -0,0 +1,74 @@
+"""
+Generalized nCr (combinations) calculator for real numbers n and integer r.
+Wikipedia URL: https://en.wikipedia.org/wiki/Binomial_coefficient
+"""
+
+from math import factorial as math_factorial
+
+
+def nCr(n: float, r: int) -> float:
+    """
+    Compute the number of combinations (n choose r) for real n and integer r
+    using the formula:
+
+        nCr = n * (n-1) * (n-2) * ... * (n-r+1) / r!
+
+    Parameters
+    ----------
+    n : float
+        Total number of items. Can be any real number.
+    r : int
+        Number of items to choose. Must be a non-negative integer.
+
+    Returns
+    -------
+    float
+        The number of combinations.
+
+    Raises
+    ------
+    ValueError
+        If r is not an integer or r < 0
+
+    Examples
+    --------
+    >>> nCr(5, 2)
+    10.0
+    >>> nCr(5.5, 2)
+    12.375
+    >>> nCr(10, 0)
+    1.0
+    >>> nCr(0, 0)
+    1.0
+    >>> nCr(5, -1)
+    Traceback (most recent call last):
+        ...
+    ValueError: r must be a non-negative integer
+    >>> nCr(5, 2.5)
+    Traceback (most recent call last):
+        ...
+    ValueError: r must be a non-negative integer
+    """
+    if not isinstance(r, int) or r < 0:
+        raise ValueError("r must be a non-negative integer")
+
+    if r == 0:
+        return 1.0
+
+    numerator = 1.0
+    for i in range(r):
+        numerator *= n - i
+
+    denominator = math_factorial(r)
+    return numerator / denominator
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
+    # Example usage
+    n = float(input("Enter n (real number): ").strip() or 0)
+    r = int(input("Enter r (integer): ").strip() or 0)
+    print(f"nCr({n}, {r}) = {nCr(n, r)}")

From 725abb4a59aebc91e196901399b91a87e029ac8f Mon Sep 17 00:00:00 2001
From: Naman-Vasudev <naman24vasudev@gmail.com>
Date: Mon, 20 Oct 2025 15:09:32 +0530
Subject: [PATCH 2/5] Update ncr_combinations.py

---
 maths/ncr_combinations.py | 50 +++++++++++++++++++--------------------
 1 file changed, 25 insertions(+), 25 deletions(-)

diff --git a/maths/ncr_combinations.py b/maths/ncr_combinations.py
index ebe17735a32c..ca24b44afcb7 100644
--- a/maths/ncr_combinations.py
+++ b/maths/ncr_combinations.py
@@ -1,24 +1,24 @@
 """
-Generalized nCr (combinations) calculator for real numbers n and integer r.
+Generalized combinations (n choose r) calculator for real total and integer choose.
 Wikipedia URL: https://en.wikipedia.org/wiki/Binomial_coefficient
 """
 
 from math import factorial as math_factorial
 
 
-def nCr(n: float, r: int) -> float:
+def combinations(total: float, choose: int) -> float:
     """
-    Compute the number of combinations (n choose r) for real n and integer r
+    Compute the number of combinations (total choose choose) for real total and integer choose
     using the formula:
 
-        nCr = n * (n-1) * (n-2) * ... * (n-r+1) / r!
+        combinations = total * (total-1) * ... * (total-choose+1) / choose!
 
     Parameters
     ----------
-    n : float
+    total : float
         Total number of items. Can be any real number.
-    r : int
-        Number of items to choose. Must be a non-negative integer.
+    choose : int
+        Number of items to select. Must be a non-negative integer.
 
     Returns
     -------
@@ -28,38 +28,38 @@ def nCr(n: float, r: int) -> float:
     Raises
     ------
     ValueError
-        If r is not an integer or r < 0
+        If choose is not a non-negative integer.
 
     Examples
     --------
-    >>> nCr(5, 2)
+    >>> combinations(5, 2)
     10.0
-    >>> nCr(5.5, 2)
+    >>> combinations(5.5, 2)
     12.375
-    >>> nCr(10, 0)
+    >>> combinations(10, 0)
     1.0
-    >>> nCr(0, 0)
+    >>> combinations(0, 0)
     1.0
-    >>> nCr(5, -1)
+    >>> combinations(5, -1)
     Traceback (most recent call last):
         ...
-    ValueError: r must be a non-negative integer
-    >>> nCr(5, 2.5)
+    ValueError: choose must be a non-negative integer
+    >>> combinations(5, 2.5)
     Traceback (most recent call last):
         ...
-    ValueError: r must be a non-negative integer
+    ValueError: choose must be a non-negative integer
     """
-    if not isinstance(r, int) or r < 0:
-        raise ValueError("r must be a non-negative integer")
+    if not isinstance(choose, int) or choose < 0:
+        raise ValueError("choose must be a non-negative integer")
 
-    if r == 0:
+    if choose == 0:
         return 1.0
 
     numerator = 1.0
-    for i in range(r):
-        numerator *= n - i
+    for i in range(choose):
+        numerator *= total - i
 
-    denominator = math_factorial(r)
+    denominator = math_factorial(choose)
     return numerator / denominator
 
 
@@ -69,6 +69,6 @@ def nCr(n: float, r: int) -> float:
     doctest.testmod()
 
     # Example usage
-    n = float(input("Enter n (real number): ").strip() or 0)
-    r = int(input("Enter r (integer): ").strip() or 0)
-    print(f"nCr({n}, {r}) = {nCr(n, r)}")
+    total_input = float(input("Enter total (real number): ").strip() or 0)
+    choose_input = int(input("Enter choose (integer): ").strip() or 0)
+    print(f"combinations({total_input}, {choose_input}) = {combinations(total_input, choose_input)}")

From ab5dfe38193f7376eaad5dfa4eba35e3a8817f1e Mon Sep 17 00:00:00 2001
From: Naman-Vasudev <naman24vasudev@gmail.com>
Date: Mon, 20 Oct 2025 15:10:34 +0530
Subject: [PATCH 3/5] Update ncr_combinations.py

---
 maths/ncr_combinations.py | 10 +++++++---
 1 file changed, 7 insertions(+), 3 deletions(-)

diff --git a/maths/ncr_combinations.py b/maths/ncr_combinations.py
index ca24b44afcb7..5fded68c8f2d 100644
--- a/maths/ncr_combinations.py
+++ b/maths/ncr_combinations.py
@@ -1,6 +1,7 @@
 """
 Generalized combinations (n choose r) calculator for real total and integer choose.
-Wikipedia URL: https://en.wikipedia.org/wiki/Binomial_coefficient
+Wikipedia URL:
+https://en.wikipedia.org/wiki/Binomial_coefficient
 """
 
 from math import factorial as math_factorial
@@ -70,5 +71,8 @@ def combinations(total: float, choose: int) -> float:
 
     # Example usage
     total_input = float(input("Enter total (real number): ").strip() or 0)
-    choose_input = int(input("Enter choose (integer): ").strip() or 0)
-    print(f"combinations({total_input}, {choose_input}) = {combinations(total_input, choose_input)}")
+    choose_input = int(input("Enter choose (non-negative integer): ").strip() or 0)
+    print(
+        f"combinations({total_input}, {choose_input}) = "
+        f"{combinations(total_input, choose_input)}"
+    )

From c15888afbdc4d5ab4a30c1433246817a206983e2 Mon Sep 17 00:00:00 2001
From: Naman-Vasudev <naman24vasudev@gmail.com>
Date: Mon, 20 Oct 2025 15:11:48 +0530
Subject: [PATCH 4/5] Update ncr_combinations.py

---
 maths/ncr_combinations.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/maths/ncr_combinations.py b/maths/ncr_combinations.py
index 5fded68c8f2d..7b7a0d37ea9a 100644
--- a/maths/ncr_combinations.py
+++ b/maths/ncr_combinations.py
@@ -9,7 +9,7 @@
 
 def combinations(total: float, choose: int) -> float:
     """
-    Compute the number of combinations (total choose choose) for real total and integer choose
+    Compute the number of combinations 
     using the formula:
 
         combinations = total * (total-1) * ... * (total-choose+1) / choose!

From 16cab8cb89f928cc165cfee7ee60e6861cd717b2 Mon Sep 17 00:00:00 2001
From: Naman-Vasudev <naman24vasudev@gmail.com>
Date: Mon, 20 Oct 2025 15:13:47 +0530
Subject: [PATCH 5/5] Update ncr_combinations.py

---
 maths/ncr_combinations.py | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/maths/ncr_combinations.py b/maths/ncr_combinations.py
index 7b7a0d37ea9a..49add3259804 100644
--- a/maths/ncr_combinations.py
+++ b/maths/ncr_combinations.py
@@ -9,8 +9,7 @@
 
 def combinations(total: float, choose: int) -> float:
     """
-    Compute the number of combinations 
-    using the formula:
+    Compute the number of combinations using the formula:
 
         combinations = total * (total-1) * ... * (total-choose+1) / choose!