Add generalized nCr (combinations) calculator for real n and integer r

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)}")