There are 5vgirls and 5 boys in a chess club. The club holds a round-robin tournament in which every player plays against every other player exactly once.
In how many games does a girl play against another girl?
To see this, note that the 5th girl plays 4 other girls
The 4th girl plays 3 other girls
The 3rd girl plays 2 other girls
The second girl plays 1 other girl
So...4 + 3 + 2 + 1 = 10
Another way to see this is to count the number of sets formed by choosing any 2 girls from 5....this is
C(5, 2) = 10