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6 Permutations of 3

Enter your n and r values below:

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

  
Evaluate the following permutation
6P3

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 = 6 and r = 3

6P3  2  6!
  (6 - 3)!

Factorial Formula:

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

Calculate n!:

n! = 6!
6! = 6 x 5 x 4 x 3 x 2 x 1
6! = 720

Calculate (n - r)!:

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

Calculate 6P3:

6P3  =  720
  6




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Excel or Google Sheets formula:

=PERMUT(6,3)


What is the Answer?

6P3 = 120

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

  1. 10 permutations of 6
  2. 5 combinations of 3
  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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