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Suppose there are 19 marbles in a bag: 5 red, 6 green, and 8 blue ones. How many ways can 5 marbles be selected if exactly 2 marbles are red and 3 are another color?

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I'm not really sure what the title of the post is asking. If you want to choose $5$ marbles, $2$ of which are red and $3$ of which are not red, then there are no repetitions here. You need the Multiplication principle here ( – JavaMan Jan 18 '12 at 4:14
Maybe, it's also good to ask, whether OP is aware of the principle of inclusion-exclusion‌​? – user21436 Jan 18 '12 at 4:17
up vote 3 down vote accepted

This is a simple problem, and you don't need inclusion-exclusion, removing repetitions, and the like.

# of ways = (ways to select 2 red)*(ways to select any 3 of other colors)

= C(5,2)*C(14,3)

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I won't downvote, but for future reference I think that giving answers outright should be discouraged, especially when the OP has yet to respond to comments in the OP can discuss the problem. – JavaMan Jan 18 '12 at 4:44
@JavaMan: Ok, i'm new to this forum. I'll bear it in mind. – true blue anil Jan 18 '12 at 6:27

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