10 Combinations of 4

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

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

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

Plugging in our numbers of n = 10 and r = 4, we get:
10C4 =10!
4!(10 - 4)!

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 first denominator (n - r)!:
(n - r)! = (10 - 4)!
(10 - 4)! = 6!
6! = 6 x 5 x 4 x 3 x 2 x 1
6! = 720

Calculate the second denominator r!:
r! = 4!
4! = 4 x 3 x 2 x 1
4! = 24

Now calculate our combination value nCr for n = 10 and r = 4:
10C4 =3,628,800
24 x 720

10C4 =3,628,800
17,280

10C4 = 210

In Microsoft Excel or , you write this function as =COMBIN(10,4)