# How Many Possible Unique Sets?

1. Oct 17, 2009

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1. The problem statement, all variables and given/known data
There are 10 cups and 40 balls. The balls come in four different colors and there are 10 of each color. If 10 of the 40 balls are placed in the 10 cups, how many unique color sets are possible?

2. Relevant equations

3. The attempt at a solution
Okay. There are 10 cups. Each cup has four different possibilities. The problem is that many arrangements are mere permutations of the same set, so my equation $$n = 4^{10}$$ doesn't hold any water.