maths.binomial_coefficient
==========================

.. py:module:: maths.binomial_coefficient


Functions
---------

.. autoapisummary::

   maths.binomial_coefficient.binomial_coefficient


Module Contents
---------------

.. py:function:: binomial_coefficient(n: int, r: int) -> int

   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