10 Permutations of 5 ·

27 Jul 2024, 00:00

Evaluate the following permutation

10P5

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 = 10 and r = 5

10P5 2	10!
	(10 - 5)!

Factorial Formula:

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

Calculate n!:

n! = 10!

10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

10! = 3,628,800

Calculate (n - r)!:

(n - r)! = (10 - 5)!

(10 - 5)! = 5!

5! = 5 x 4 x 3 x 2 x 1

5! = 120

Calculate 10P5:

10P5 =	3,628,800
	120

10P5 = 30,240

Excel or Google Sheets formula:

=PERMUT(10,5)

What is the Answer?

10P5 = 30,240

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

10 Permutations of 5

Evaluate the following permutation 10P5 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! = 10! 10! = 10 x 9 x 8 x 7 x 6 x 5 x