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Evaluate the combination:

₁₄C₁₂

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 = 14 and r = 12

14C12  2	14!
	12!(14 - 12)!

Factorial Formula:

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

Calculate the numerator n!:

n! = 14!

14! = 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

14! = 87,178,291,200

Calculate (n - r)!:

(n - r)! = (14 - 12)!

(14 - 12)! = 2!

2! = 2 x 1

2! = 2

Calculate r!:

r! = 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 ₁₄C₁₂

14C12  =	87,178,291,200
	479,001,600 x 2

14C12  =	87,178,291,200
	958,003,200

₁₄C₁₂ = 91

You have 1 free calculations remaining

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Excel or Google Sheets formula:

Excel or Google Sheets formula:=COMBIN(14,12)

What is the Answer?

₁₄C₁₂ = 91

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 = _nP_r
Number of combination(s) of n items arranged in r unique ways = _nC_r 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
_nP_r = 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.
_nP_r = n!/(n - r)!

permutations and combinations

Example calculations for the Permutations and Combinations Calculator

Permutations and Combinations Calculator Video

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