maths.ncr_combinations
======================

.. py:module:: maths.ncr_combinations

.. autoapi-nested-parse::

   Generalized combinations (n choose r) calculator for real total and integer choose.
   Wikipedia URL:
   https://en.wikipedia.org/wiki/Binomial_coefficient



Attributes
----------

.. autoapisummary::

   maths.ncr_combinations.total_input


Functions
---------

.. autoapisummary::

   maths.ncr_combinations.combinations


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

.. py:function:: combinations(total: float, choose: int) -> float

   Compute the number of combinations using the formula:

       combinations = total * (total-1) * ... * (total-choose+1) / choose!

   Parameters
   ----------
   total : float
       Total number of items. Can be any real number.
   choose : int
       Number of items to select. Must be a non-negative integer.

   Returns
   -------
   float
       The number of combinations.

   Raises
   ------
   ValueError
       If choose is not a non-negative integer.

   Examples
   --------
   >>> combinations(5, 2)
   10.0
   >>> combinations(5.5, 2)
   12.375
   >>> combinations(10, 0)
   1.0
   >>> combinations(0, 0)
   1.0
   >>> combinations(5, -1)
   Traceback (most recent call last):
       ...
   ValueError: choose must be a non-negative integer
   >>> combinations(5, 2.5)
   Traceback (most recent call last):
       ...
   ValueError: choose must be a non-negative integer


.. py:data:: total_input