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- Aug 18, 2013

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Or another way to think of it is you're "choosing" 12 marbles out of a bag at random. There are a few separate cases you have to consider:

Case #1: Choosing all 4 red marbles out of the bag at once.

Case #2a: Not choosing any red marbles out of the bag, and choosing another 12 marbles, with all 4 of the red marbles in that group.

Case #2b: Not choosing any red marbles out of the bag, then choosing another 12 marbles and not getting any red marbles out of that either.

Find the probabilities of each of these cases and then add them.