l 10 Permutations of 5

Enter n

Enter r

  

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!

Calculate (n - r)!:

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

(10 - 5)! = 5!

Calculate 10P5:

10P5  =  10 x 9 x 8 x 7 x 6 x 5!
  5!

10P5  =  10 x 9 x 8 x 7 x 6 x 5!
  5!

10P5 = 10 x 9 x 8 x 7 x 6

Final Answer


10P5 = 30,240