Tried new TESTS for the binomial_coefficient (TheAlgorithms#10822)

* Tried new TESTS for the binomial_coefficient

* Fix the tests request

* Update binomial_coefficient.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

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* Update binomial_coefficient.py

---------

Co-authored-by: Christian Clauss <cclauss@me.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

Author: 3 people

maths/binomial_coefficient.py

@@ -1,10 +1,48 @@
 def binomial_coefficient(n: int, r: int) -> int:
     """
-    Find binomial coefficient using pascals triangle.
+    Find binomial coefficient using Pascal's triangle.
+
+    Calculate C(n, r) using Pascal's triangle.
+
+    :param n: The total number of items.
+    :param r: The number of items to choose.
+    :return: The binomial coefficient C(n, r).
 
     >>> binomial_coefficient(10, 5)
     252
+    >>> binomial_coefficient(10, 0)
+    1
+    >>> binomial_coefficient(0, 10)
+    1
+    >>> binomial_coefficient(10, 10)
+    1
+    >>> binomial_coefficient(5, 2)
+    10
+    >>> binomial_coefficient(5, 6)
+    0
+    >>> binomial_coefficient(3, 5)
+    0
+    >>> binomial_coefficient(-2, 3)
+    Traceback (most recent call last):
+        ...
+    ValueError: n and r must be non-negative integers
+    >>> binomial_coefficient(5, -1)
+    Traceback (most recent call last):
+        ...
+    ValueError: n and r must be non-negative integers
+    >>> binomial_coefficient(10.1, 5)
+    Traceback (most recent call last):
+        ...
+    TypeError: 'float' object cannot be interpreted as an integer
+    >>> binomial_coefficient(10, 5.1)
+    Traceback (most recent call last):
+        ...
+    TypeError: 'float' object cannot be interpreted as an integer
     """
+    if n < 0 or r < 0:
+        raise ValueError("n and r must be non-negative integers")
+    if 0 in (n, r):
+        return 1
     c = [0 for i in range(r + 1)]
     # nc0 = 1
     c[0] = 1
@@ -17,4 +55,8 @@ def binomial_coefficient(n: int, r: int) -> int:
     return c[r]
 
 
-print(binomial_coefficient(n=10, r=5))
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()
+    print(binomial_coefficient(n=10, r=5))