12 Combinations of 5

<-- 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 = 12 and r = 5, we get:
12C5 =12!
5!(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 first 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

Calculate the second denominator r!:
r! = 5!
5! = 5 x 4 x 3 x 2 x 1
5! = 120

Now calculate our combination value nCr for n = 12 and r = 5:
12C5 =479,001,600
120 x 5,040

12C5 =479,001,600
604,800

12C5 = 792

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