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

How many sets of four marbles include all the red ones?

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    $\begingroup$ I've added the tag combinatorics, which is more suitable. Probably you want to use the result in finding some probability, but the question itself is a combinatorial one. $\endgroup$ Apr 17, 2012 at 20:45

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You have four elements out of which three are red. So you can complete the last position with any of the balls of other colors.

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Without repetition you have 4 colours apart from red so: $4$ ways to add a marble to a set of 3 red ones and therefore $4$ different sets with 3 red marbles.

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If a set of 4 contains all 3 reds, it can contain just one other as well. There are 13 other marbles, so there are 13 sets of 4 that contain all the reds.

I see that other people have said "4 sets", because there are 4 other colours. The wording of the question is a bit vague.

If you had 3 reds and one green, there's no argument about that being one set. But suppose you now exchanged that green marble for another green marble. Would that then be the same set? I say it wouldn't, but obviously other people think it would.

I'm not giving a "thumbs down" to anyone who disagrees with me, and I would ask others to treat me the same.

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  • $\begingroup$ Actually only one other answer takes the stand that all the marbles of a same color should count as one, so you could be a bit more relaxed about other people, thumbs down, and so on. $\endgroup$
    – Did
    May 7, 2012 at 6:49

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