20 Permutations of 3

May 2024 ยท 2 minute read
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Evaluate the following permutation

20P3

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 = 20 and r = 3
20P3  2  20!
  (20 - 3)!

Factorial Formula:

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

Calculate n!:

n! = 20!

20! = 20 x 19 x 18 x 17 x 16 x 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

20! = 2,432,902,008,176,640,000

Calculate (n - r)!:

(n - r)! = (20 - 3)!

(20 - 3)! = 17!

17! = 17 x 16 x 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

17! = 355,687,428,096,000

Calculate 20P3:
20P3  =  2,432,902,008,176,640,000
  355,687,428,096,000

20P3 = 6,840


Excel or Google Sheets formula:

=PERMUT(20,3)

What is the Answer?

20P3 = 6,840

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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