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Math Help - Pigeon Hole Principle

  1. #1
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    Pigeon Hole Principle

    Hey guys, the Pigeon Hole principle seems relatively easy to understand but when it comes to examples/problems I don't quite understand.

    For example this problem:
    a drawer contains a dozen browns and dozen black socks, all unmatched.
    A man takes out a sock at random.
    a) How many socks must he take out to be sure that he has at least two socks of the same color? This I understand is 3 because the first two may be different but if he gets another one, he would a pair of same color.

    but this part I'm confuse.
    b)How many socks must he take out to be sure that he has at least two black socks? The answer is 14 but Im not sure how it is 14. If anyone can explain how it is 14 and the reason behind it would be greatly appreciated.

    Thank You in advance.
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  2. #2
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    Suppose that you draw a black sock first.
    You draw a brown sock on each of the next twelve draws.
    How many draws does it take to get two black socks
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