4 Combinations of 3

<-- 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 = 4 and r = 3, we get:
4C3 =4!
3!(4 - 3)!

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

Calculate the numerator n!:
n! = 4!
4! = 4 x 3 x 2 x 1
4! = 24

Calculate the first denominator (n - r)!:
(n - r)! = (4 - 3)!
(4 - 3)! = 1!
1! = 1
1! = 1

Calculate the second denominator r!:
r! = 3!
3! = 3 x 2 x 1
3! = 6

Now calculate our combination value nCr for n = 4 and r = 3:
4C3 =24
6 x 1

4C3 =24
6

4C3 = 4

In Microsoft Excel or , you write this function as =COMBIN(4,3)