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

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

Calculate the numerator n!:
n! = 3!
3! = 3 x 2 x 1
3! = 6

Calculate the first denominator (n - r)!:
(n - r)! = (3 - 3)!
(3 - 3)! = 0!
0! =
0! = 1

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

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

3C3 =6
6

3C3 = 1

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