Sample inputs

n: 10
r: 4

n: 5
r: 2

n: 14
r: 10

How to Calculate Number of Combinations?

Follow these steps to calculate the number of combinations to select r number of objects from a total of n number of objects.

1. Get the value of n (total number of objects), and r (sample size).
2. The Combination Formula to get the possible number of combinations to select r number of objects from a total of n number of objects is:

   \({{}^{n}C_{r}} = \frac{n!}{r!(n-r)!}\)

3. Substitute the values of given n and r in the above formula.
4. Compute the factorials, and simplify the right hand side value.

   where

   \(n! = 1\cdot 2 \cdot 3 ~ \cdots ~ (n-1) \cdot n \)