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Math Help - Permutations - Forming Committee of 5 from 8 people with Restrictions

  1. #1
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    Permutations - Forming Committee of 5 from 8 people with Restrictions

    Hi guys, need help with this question:

    In how many ways can a committee of 5 be formed from a group of 8 people consisting of 3 boys, 3 girls and a brother-sister pair if
    (i) the committee must include the brother-sister pair?
    (ii) one girl A refuses to serve in the same committee with a particular boy?

    (i) No. of ways (for remaining 3 ppl) = 6C3 * 3!
    I am not sure how to include the brother-sister pair, is it just mutiply the above by (1 * 2!) ?
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  2. #2
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    Re: Permutations - Forming Committee of 5 from 8 people with Restrictions

    Quote Originally Posted by Blizzardy View Post
    In how many ways can a committee of 5 be formed from a group of 8 people consisting of 3 boys, 3 girls and a brother-sister pair if
    (i) the committee must include the brother-sister pair?
    (ii) one girl A refuses to serve in the same committee with a particular boy?
    Why have you used permutations here?

    The number of committees is determined by combinations. A committee is determined only by its content, who is on it. The order in which the members the members are chosen has nothing to do with it.

    So to answer part (ii): Count the number of committees with girl A and not the boy, then add to that the number of committees without girl A.
    \binom{6}{4}+\binom{7}{5} .
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  3. #3
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    Re: Permutations - Forming Committee of 5 from 8 people with Restrictions

    (i)

    If the brother-sister pair "must" be included,
    you may consider them already selected
    and the problem boils down to selecting 3 from the remaining 6 without restriction.
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