5 Combinations of 0

<-- 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 = 5 and r = 0, we get:
5C0 =5!
0!(5 - 0)!

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

Calculate the numerator n!:
n! = 5!
5! = 5 x 4 x 3 x 2 x 1
5! = 120

Calculate the first denominator (n - r)!:
(n - r)! = (5 - 0)!
(5 - 0)! = 5!
5! = 5 x 4 x 3 x 2 x 1
5! = 120

Calculate the second denominator r!:
r! = 0!
0! =
0! = 1

Now calculate our combination value nCr for n = 5 and r = 0:
5C0 =120
1 x 120

5C0 =120
120

5C0 = 1

In Microsoft Excel or , you write this function as =COMBIN(5,0)