Evaluate the following permutation

90P5

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 = 90 and r = 5

90P5  2	90!
	(90 - 5)!

Factorial Formula:

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

Calculate n!:

n! = 90!

90! = 90 x 89 x 88 x 87 x 86 x 85 x 84 x 83 x 82 x 81 x 80 x 79 x 78 x 77 x 76 x 75 x 74 x 73 x 72 x 71 x 70 x 69 x 68 x 67 x 66 x 65 x 64 x 63 x 62 x 61 x 60 x 59 x 58 x 57 x 56 x 55 x 54 x 53 x 52 x 51 x 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

90! = 1,485,715,964,481,760,688,598,126,444,658,390,468,648,504,385,338,494,631,194,665,214,503,009,929,244,428,884,407,664,620,677,918,947,601,692,538,663,274,334,960,161,140,774,153,486,336

Calculate (n - r)!:

(n - r)! = (90 - 5)!

(90 - 5)! = 85!

85! = 85 x 84 x 83 x 82 x 81 x 80 x 79 x 78 x 77 x 76 x 75 x 74 x 73 x 72 x 71 x 70 x 69 x 68 x 67 x 66 x 65 x 64 x 63 x 62 x 61 x 60 x 59 x 58 x 57 x 56 x 55 x 54 x 53 x 52 x 51 x 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

85! = 281,710,411,438,054,936,145,340,070,063,731,769,270,618,697,594,701,234,453,923,080,571,636,972,801,512,907,171,791,271,651,453,851,961,008,097,129,997,800,044,545,179,648

Calculate 90P5:

90P5  =	1,485,715,964,481,760,688,598,126,444,658,390,468,648,504,385,338,494,631,194,665,214,503,009,929,244,428,884,407,664,620,677,918,947,601,692,538,663,274,334,960,161,140,774,153,486,336
	281,710,411,438,054,936,145,340,070,063,731,769,270,618,697,594,701,234,453,923,080,571,636,972,801,512,907,171,791,271,651,453,851,961,008,097,129,997,800,044,545,179,648

90P5 = 5,273,912,160

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Excel or Google Sheets formula:

Excel or Google Sheets formula:=PERMUT(90,5)

What is the Answer?

90P5 = 5,273,912,160

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

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