Question

Navid took a trip to the store to
purchase some balls. His
choices at the store were
green,blue,white and red
balls. If Navid purchased 9 balls, how many different
combinations of balls could he
have purchased?

Answer 1

This amounts to coloring 9 balls with 4 colors. We can represent a coloring as a string of 9 o's and 3 |'s. E.g.

000|00|000|0

represents 3 balls with color 1, 2 balls with color 2, 3 balls with color 3 and 1 ball with color 4. The number of different strings you can make is:

12!/(9! 3!) = 12*11*10/(3*2) = 220