10 Permutations of 6

Enter your n and r values below:

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Evaluate the following permutation
10P6

Permutation Definition:

An order or arrangement

Permutation Formula:

nPr  =  n!
  (n - r)!

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

Plug in n = 10 and r = 6

10P6  2  10!
  (10 - 6)!

Factorial Formula:

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

Calculate n!:

n! = 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 (n - r)!:

(n - r)! = (10 - 6)!
(10 - 6)! = 4!
4! = 4 x 3 x 2 x 1
4! = 24

Calculate 10P6:

10P6  =  3,628,800
  24




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Excel or Google Sheets formula:

=PERMUT(10,6)


What is the Answer?

10P6 = 151,200

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 = 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

Example calculations for the Permutations and Combinations Calculator

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  3. 9 combination 4
  4. 8 combination 2
  5. 6 permutation 2
  6. 10 permutations of 5
  7. 6P3
  8. 7c4
  9. how many subsets of at least 3 elements can be formed from a set of 4 elements

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