7 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 = 7 and r = 4, we get:
7C4 =7!
4!(7 - 4)!

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

Calculate the numerator n!:
n! = 7!
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1
7! = 5,040

Calculate the first denominator (n - r)!:
(n - r)! = (7 - 4)!
(7 - 4)! = 3!
3! = 3 x 2 x 1
3! = 6

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 = 7 and r = 4:
7C4 =5,040
24 x 6

7C4 =5,040
144

7C4 = 35

In Microsoft Excel or , you write this function as =COMBIN(7,4)