8 Combinations of 2

<-- 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 = 8 and r = 2, we get:
8C2 =8!
2!(8 - 2)!

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

Calculate the numerator n!:
n! = 8!
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
8! = 40,320

Calculate the first denominator (n - r)!:
(n - r)! = (8 - 2)!
(8 - 2)! = 6!
6! = 6 x 5 x 4 x 3 x 2 x 1
6! = 720

Calculate the second denominator r!:
r! = 2!
2! = 2 x 1
2! = 2

Now calculate our combination value nCr for n = 8 and r = 2:
8C2 =40,320
2 x 720

8C2 =40,320
1,440

8C2 = 28

In Microsoft Excel or , you write this function as =COMBIN(8,2)