45 Permutations of 3 ·

12 Jul 2024, 00:00

Evaluate the following permutation

45P3

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 = 45 and r = 3

45P3 2	45!
	(45 - 3)!

Factorial Formula:

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

Calculate n!:

n! = 45!

45! = 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

45! = 119,622,220,865,480,188,574,992,723,157,469,373,503,186,265,858,579,103,744

Calculate (n - r)!:

(n - r)! = (45 - 3)!

(45 - 3)! = 42!

42! = 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

42! = 1,405,006,117,752,879,788,779,635,797,590,784,832,178,972,610,527,232

Calculate 45P3:

45P3 =	119,622,220,865,480,188,574,992,723,157,469,373,503,186,265,858,579,103,744
	1,405,006,117,752,879,788,779,635,797,590,784,832,178,972,610,527,232

45P3 = 85,140

You have 1 free calculations remaining

Excel or Google Sheets formula:

Excel or Google Sheets formula:=PERMUT(45,3)

What is the Answer?

45P3 = 85,140

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

45 Permutations of 3

Evaluate the following permutation 45P3 An order or arrangement where n is the number of itemsr is the number of arrangements. n! = n * (n - 1) * (n - 2) * .... * 2 * 1 n! = 45! 45! = 45 x 44 x 43 x 42 x 41 x 40 x