3 Combinations of 2

<-- 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 = 2, we get:
3C2 =3!
2!(3 - 2)!

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 - 2)!
(3 - 2)! = 1!
1! = 1
1! = 1

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

Now calculate our combination value nCr for n = 3 and r = 2:
3C2 =6
2 x 1

3C2 =6
2

3C2 = 3

In Microsoft Excel or , you write this function as =COMBIN(3,2)