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Thread: Combination Question

  1. #1
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    Combination Question

    Question:
    There are ten possible players for the VI to represent a tennis club and of these the captain and the secretary must be in the team. In how many ways can the team be selected?

    there is 6 places as VI = 6

    10 players (includes captain & secretary)

    C S _ _ _ _
    there is 4 spaces to fill thus
    the amount of ways;
    2 x 8C4 = 140

    there are 140 ways

    the text book states the answer is 70

    Did I make a mistake by multiplying 8C4 by 2?


    thank you for helping
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  2. #2
    Member Walagaster's Avatar
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    Re: Combination Question

    Yes, that is the mistake. There are 2C2 = 1 ways of picking the two required people, not 2 ways.
    Thanks from bigmansouf
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