55 Permutations of 3

Evaluate the following permutation

₅₅P₃

Permutation Definition:

An order or arrangement

Permutation Formula:

_nP_r =	n!
	(n - r)!

where n is the number of items
r is the number of arrangements.

Plug in n = 55 and r = 3

₅₅P₃ 2	55!
	(55 - 3)!

Factorial Formula:

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

Calculate n!:

n! = 55!

55! = 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

55! = 12,696,403,353,658,276,446,882,823,840,816,011,312,245,221,598,828,319,560,272,916,152,712,167,424

Calculate (n - r)!:

(n - r)! = (55 - 3)!

(55 - 3)! = 52!

52! = 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

52! = 80,658,175,170,943,876,845,634,591,553,351,679,477,960,544,579,306,048,386,139,594,686,464

Calculate 55P3:

₅₅P₃ =	12,696,403,353,658,276,446,882,823,840,816,011,312,245,221,598,828,319,560,272,916,152,712,167,424
	80,658,175,170,943,876,845,634,591,553,351,679,477,960,544,579,306,048,386,139,594,686,464

₅₅P₃ = 157,410

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Excel or Google Sheets formula:

Excel or Google Sheets formula:=PERMUT(55,3)

What is the Answer?

₅₅P₃ = 157,410

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