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Math Help - Problems

  1. #1
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    Problems

    Help please, I suck at permutations and combination.

    1.) A. In how many different ways can a student answer a 20 question true-false examination?
    B. In how many ways can he answer the examination if he is to answer 18 out of 20 questions?

    2. In how many ways can 4 male students, 4 female students and a professor sit in a row for class picture if:
    A. No restrictions?
    B. the professor must be in the middle
    C. a certain student and the professor must occupy the ends?

    3. Find the number of ways of selecting 6 balls from 6 red balls, 3 green ball and 5 black balls if each selection consists of 2 red balls, 2 green balls and 2 black balls.

    4. In how many ways can 13 people be grouped into two groups of 8 and 5 if a certain person is to be in the larger group?

    5. Ten people is to sit a round table. Three particular people insist on sitting next to each other. In how many ways can ten be seated?

    Help please, hope you can help me. Thank you very much.
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  2. #2
    Super Member Anonymous1's Avatar
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    1.
    A) 2^{20}

    B) {20\choose 18} \times 2^{18}
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  3. #3
    Super Member Anonymous1's Avatar
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    2.
    A) 9!
    B) 1!\times 8!
    C) 2!\times 7!
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  4. #4
    Super Member Anonymous1's Avatar
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    3.
     {6\choose 2}\times{3\choose 2}\times{5\choose 2}

    4.
    {13\choose 1}\times{12\choose 7}\times {5\choose 5}

    5.
    3!\times 7!^2
    Last edited by Anonymous1; March 18th 2010 at 07:08 AM.
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  5. #5
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    Quote Originally Posted by Anonymous1 View Post
    3.
     {6\choose 2}\times{3\choose 2}\times{5\choose 2}

    4.
    {1\choose 1}\times{12\choose 7}\times {5\choose 5}

    5.
    3!\times 7!^2

    what do u mean by the two numbers inside the parenthesis? divide them?
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  6. #6
    Super Member Anonymous1's Avatar
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    nCr. You know combinations..

    {n\choose k}= \frac{n!}{(n-k)!k!}
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  7. #7
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    Sorry to bother but can briefly explain some of the answers?
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  8. #8
    Super Member Anonymous1's Avatar
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    Which ones?
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  9. #9
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    Quote Originally Posted by Anonymous1 View Post
    3.
     {6\choose 2}\times{3\choose 2}\times{5\choose 2}

    4.
    {13\choose 1}\times{12\choose 7}\times {5\choose 5}

    5.
    3!\times 7!^2
    How did you get the (6 over 2) ?
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  10. #10
    Super Member Anonymous1's Avatar
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    We have six red balls. We want two of them. How many combinations of two red balls can we select when we have a group of six in total?

    6 choose 2, or {6\choose 2} = \frac{6!}{(6-2)!2!}
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  11. #11
    Super Member Bacterius's Avatar
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    The {a \choose b} notation is just a notation for this purpose, it does not mean division. It means how many combinations of b elements in a elements exist.
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