At Maryland Middle School, there are 9 mathematics classes. If two mathematics classes are selected for a school competition, what is the number of possible outcomes?

Answer 1

combinations of 2 out of 9

C(n,r) = n!/[(n-r)! (r!) ]
= 9! /[ 7! * 2! ]

= 9*8 *7! / [ 7! * 2]
=9*4
= 36

Answer 2

Or use Pascal's triangle
row 9 is
1 9 36 84 126 126 84 36 9 1

so r = 0 --> 1
r = 1 = 9 of course
r = 2 = 36