 # 15 Combinations of 5

## Enter your n and r values below:

<-- Enter (n)
<-- Enter (r)

Evaluate the combination:
15C5

## Combination Definition:

A unique order or arrangement

## Combination Formula:

 nCr  = n! r!(n - r)!

where n is the number of items
r is the unique arrangements.

## Plug in n = 15 and r = 5

 15C5  2 15! 5!(15 - 5)!

## Factorial Formula:

n! = n * (n - 1) * (n - 2) * .... * 2 * 1

## Calculate the numerator n!:

n! = 15!
15! = 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
15! = 1,307,674,368,000

## Calculate (n - r)!:

(n - r)! = (15 - 5)!
(15 - 5)! = 10!
10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
10! = 3,628,800

## Calculate r!:

r! = 5!
5! = 5 x 4 x 3 x 2 x 1
5! = 120

## Calculate 15C5

 15C5  = 1,307,674,368,000 120 x 3,628,800

 15C5  = 1,307,674,368,000 435,456,000

## Excel or Google Sheets formula:

=COMBIN(15,5)

15C5 = 3,003

### How does the Permutations and Combinations Calculator work?

Free Permutations and Combinations Calculator - Calculates the following:
Number of permutation(s) of n items arranged in r ways = nPr
Number of combination(s) of n items arranged in r unique ways = nCr including subsets of sets
This calculator has 2 inputs.

### What 2 formulas are used for the Permutations and Combinations Calculator?

1. nPr=n!/r!
2. nCr=n!/r!(n-r)!

For more math formulas, check out our Formula Dossier

### What 4 concepts are covered in the Permutations and Combinations Calculator?

combination
a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter
nPr = n!/r!(n - r)!
factorial
The product of an integer and all the integers below it
permutation
a way in which a set or number of things can be ordered or arranged.
nPr = n!/(n - r)!
permutations and combinations