# Determining the Number of Ways of Getting Marbles

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A bag contains three red marbles, three green ones, one lavender one, two yellows, and four orange marbles.

How many sets of five marbles include either the lavender one or exactly one yellow one but not both colors?

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##### Solution Summary

We use combinatorics to determine the number of ways of selecting five marbles with different specified colors from a sample of 13 marbles with specified colors.

##### Solution Preview

Let N_L be the number of sets of five marbles which include the lavender one.

Let N_Y be the number of sets of five marbles which include exactly one yellow one.

Let N_LY be the number of sets of five marbles which include the lavendar one and exactly one yellow one.

Let N be the number of sets of five marbles which include the either lavender one or exactly ...

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