50 Permutations of 3

Posted by Trudie Dory on Wednesday, June 12, 2024
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Evaluate the following permutation

50P3

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 = 50 and r = 3
50P3  2  50!
  (50 - 3)!

Factorial Formula:

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

Calculate n!:

n! = 50!

50! = 50 x 49 x 48 x 47 x 46 x 45 x 44 x 43 x 42 x 41 x 40 x 39 x 38 x 37 x 36 x 35 x 34 x 33 x 32 x 31 x 30 x 29 x 28 x 27 x 26 x 25 x 24 x 23 x 22 x 21 x 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

50! = 30,414,093,201,713,375,576,366,966,406,747,986,832,057,064,836,514,787,179,557,289,984

Calculate (n - r)!:

(n - r)! = (50 - 3)!

(50 - 3)! = 47!

47! = 47 x 46 x 45 x 44 x 43 x 42 x 41 x 40 x 39 x 38 x 37 x 36 x 35 x 34 x 33 x 32 x 31 x 30 x 29 x 28 x 27 x 26 x 25 x 24 x 23 x 22 x 21 x 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

47! = 258,623,241,511,168,177,673,491,006,652,997,026,552,325,199,826,237,836,492,800

Calculate 50P3:
50P3  =  30,414,093,201,713,375,576,366,966,406,747,986,832,057,064,836,514,787,179,557,289,984
  258,623,241,511,168,177,673,491,006,652,997,026,552,325,199,826,237,836,492,800

50P3 = 117,600

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Excel or Google Sheets formula:
Excel or Google Sheets formula:=PERMUT(50,3)

What is the Answer?

50P3 = 117,600

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

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