Enter your n and r values below:

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

Evaluate the combination:

3C2

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 = 3 and r = 2

 3C2  2 3! 2!(3 - 2)!

Factorial Formula:

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

n! = 3!

3! = 3 x 2 x 1

3! = 6

Calculate (n - r)!:

(n - r)! = (3 - 2)!

(3 - 2)! = 1!

1! = 1

1! = 1

r! = 2!

2! = 2 x 1

2! = 2

Calculate 3C2

 3C2  = 6 2 x 1

 3C2  = 6 2

3C2 = 3

Excel or Google Sheets formula:

Excel or Google Sheets formula:=COMBIN(3,2)

3C2 = 3
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