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Evaluate the following permutation

₆₉P₅

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 = 69 and r = 5

69P5  2	69!
	(69 - 5)!

Factorial Formula:

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

Calculate n!:

n! = 69!

69! = 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

69! = 171,122,452,428,141,297,375,735,434,272,073,448,876,652,721,480,628,511,030,304,905,066,123,383,956,194,496,253,690,059,725,733,888

Calculate (n - r)!:

(n - r)! = (69 - 5)!

(69 - 5)! = 64!

64! = 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

64! = 126,886,932,185,884,165,437,806,897,585,122,925,290,119,029,064,705,209,778,508,545,103,477,590,511,637,067,401,789,440

Calculate 69P5:

69P5  =	171,122,452,428,141,297,375,735,434,272,073,448,876,652,721,480,628,511,030,304,905,066,123,383,956,194,496,253,690,059,725,733,888
	126,886,932,185,884,165,437,806,897,585,122,925,290,119,029,064,705,209,778,508,545,103,477,590,511,637,067,401,789,440

₆₉P₅ = 1,348,621,560

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Excel or Google Sheets formula:

Excel or Google Sheets formula:=PERMUT(69,5)

What is the Answer?

₆₉P₅ = 1,348,621,560

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 = _nP_r
Number of combination(s) of n items arranged in r unique ways = _nC_r 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?

combination

a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter
_nP_r = n!/r!(n - r)!

factorial

The product of an integer and all the integers below it

permutation

a way in which a set or number of things can be ordered or arranged.
_nP_r = n!/(n - r)!

permutations and combinations

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