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Obviously, the number of ways to put k different elements in 10 different cells is $D(10,k)$.

However, what if the cells now have 2 different colors, say three of them are red and the rest, 7, are green, but they are still different. How can this be calculated? I thought about calculating it using combinations, where's the first ball can go either to a red cell or a green cell etc.

Thanks in advance :)

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