15 Permutations of 8

Evaluate the following permutation
₁₅P₈

Permutation Definition:

An order or arrangement

Permutation Formula:

_nP_r =	n!
	(n - r)!

where n is the number of items
r is the number of arrangements.

Plug in n = 15 and r = 8

₁₅P₈ 2	15!
	(15 - 8)!

Factorial Formula:

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

Calculate n!:

n! = 15!
15! = 15 x 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
15! = 1,307,674,368,000

Calculate (n - r)!:

(n - r)! = (15 - 8)!
(15 - 8)! = 7!
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1
7! = 5,040

Calculate 15P8:

₁₅P₈ =	1,307,674,368,000
	5,040

Excel or Google Sheets formula:

=PERMUT(15,8)

What is the Answer?

₁₅P₈ = 259,459,200

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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