10 Permutations of 6

<-- 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.

10P6 =10!
(10 - 6)!

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

Calculate the numerator 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 the denominator (n - r)!:
(n - r)! = (10 - 6)!
(10 - 6)! = 4!
4! = 4 x 3 x 2 x 1
4! = 24

Now calculate our permutation value nPr for n = 10 and r = 6:
10P6 =3,628,800
24

10P6 = 151,200

In Microsoft Excel or , you write this function as =PERMUT(10,6)