12 Permutations of 5

<-- Enter Number of Items (n)
<-- Enter Number of Arrangements (r)

The formula for a combination of choosing r ways from n possibilities is:
nPr =n!
(n - r)!

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

12P5 =12!
(12 - 5)!

Remember from our factorial lesson that n! = n * (n - 1) * (n - 2) * .... * 2 * 1

Calculate the numerator n!:
n! = 12!
12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
12! = 479,001,600

Calculate the denominator (n - r)!:
(n - r)! = (12 - 5)!
(12 - 5)! = 7!
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1
7! = 5,040

Now calculate our permutation value nPr for n = 12 and r = 5:
12P5 =479,001,600
5,040

12P5 = 95,040

In Microsoft Excel or , you write this function as =PERMUT(12,5)