5 Permutations of 2

Publish date: 2024-06-05
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Evaluate the following permutation

5P2

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 = 5 and r = 2
5P2  2  5!
  (5 - 2)!

Factorial Formula:

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

Calculate n!:

n! = 5!

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

5! = 120

Calculate (n - r)!:

(n - r)! = (5 - 2)!

(5 - 2)! = 3!

3! = 3 x 2 x 1

3! = 6

Calculate 5P2:
5P2  =  120
  6

5P2 = 20


Excel or Google Sheets formula:

=PERMUT(5,2)

What is the Answer?

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?

combinationa 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)!factorialThe product of an integer and all the integers below itpermutationa 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

Permutations and Combinations Calculator Video


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