Heather has 6 CDs that she is going to give away. She lets her best friend choose 2 of the 6 CDs. How many different groups of 2 CDs are possible?

Question

Heather has
6
CDs that she is going to give away. She lets her best friend choose
2
of the
6
CDs. How many different groups of
2
CDs are possible?

Answer 1

15 possibilities since order doesn't matter.

CD 1 and CD 2 is same as CD 2 and CD 1

 

1 with 2,3,4,5,6 = 5 pairs

2 with 3,4,5,6 = 4 pairs

3 with 4,5,6 = 3 pairs

4 with 5,6 = 2 pairs

5,6 = 1 pair

--------------------------------

15 possible pairs

 

The formula for combinations of n things taken k at a time

ⁿC_k = [n(n-1)(n-2).... up to k factors]/k!

 

n = 6, k = 2

 

⁶C₂ = [(6)(5)]/2! = 30/2 = 15