Evaluate the following permutation
21P4
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 = 21 and r = 4
| 21P4 2 | 21! |
| (21 - 4)! |
Factorial Formula:
n! = n * (n - 1) * (n - 2) * .... * 2 * 1
Calculate n!:
n! = 21!
21! = 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
21! = 51,090,942,171,709,440,000
Calculate (n - r)!:
(n - r)! = (21 - 4)!
(21 - 4)! = 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 21P4:
| 21P4 = | 51,090,942,171,709,440,000 |
| 355,687,428,096,000 |
21P4 = 143,640
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Excel or Google Sheets formula:
Excel or Google Sheets formula:=PERMUT(21,4)What is the Answer?
21P4 = 143,640
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 matternPr = 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
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