Enter your n and r values below:

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

Evaluate the combination:

12C10

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 = 10

 12C10  2 12! 10!(12 - 10)!

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 - 10)!

(12 - 10)! = 2!

2! = 2 x 1

2! = 2

Calculate r!:

r! = 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 12C10

 12C10  = 479,001,600 3,628,800 x 2

 12C10  = 479,001,600 7,257,600

12C10 = 66

12C10 = 66
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?

nPr=n!/r!
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