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You are given a sack containing $n$ red balls and $n$ blue balls. You take the balls out of the sack one by one and write down the sequence of reds and blues you get. How many sequences are possible?

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up vote 3 down vote accepted

HINT: A sequence is completely determined by the position in it of the $n$ red balls: once you know where they are, you also know where the blue balls are. How many different sets of $n$ positions are there in a string of $2n$ positions?

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I thought it was more difficult than it is. – Herp Derpington Nov 8 '12 at 9:28
@Herp: Combinatorics problems can be deceptive in either direction. – Brian M. Scott Nov 8 '12 at 9:42

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