 # 12 Combinations of 4

## Enter your n and r values below:

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

Evaluate the combination:
12C4

## 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 = 12 and r = 4

 12C4  2 12! 4!(12 - 4)!

## Factorial Formula:

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

## Calculate the numerator n!:

n! = 12!
12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
12! = 479,001,600

## Calculate (n - r)!:

(n - r)! = (12 - 4)!
(12 - 4)! = 8!
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
8! = 40,320

## Calculate r!:

r! = 4!
4! = 4 x 3 x 2 x 1
4! = 24

## Calculate 12C4

 12C4  = 479,001,600 24 x 40,320

 12C4  = 479,001,600 967,680

## Excel or Google Sheets formula:

=COMBIN(12,4)

12C4 = 495

### 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