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Evaluate the combination:

₁₂C₅

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 = 5

12C5  2	12!
	5!(12 - 5)!

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 - 5)!

(12 - 5)! = 7!

7! = 7 x 6 x 5 x 4 x 3 x 2 x 1

7! = 5,040

Calculate r!:

r! = 5!

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

5! = 120

Calculate ₁₂C₅

12C5  =	479,001,600
	120 x 5,040

12C5  =	479,001,600
	604,800

₁₂C₅ = 792

You have 1 free calculations remaining

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Excel or Google Sheets formula:

Excel or Google Sheets formula:=COMBIN(12,5)

What is the Answer?

₁₂C₅ = 792

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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