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Math Help - discrete math (permutation,combination and circular) Part 1 questions

  1. #1
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    discrete math (permutation,combination and circular) Part 1 questions

    A box contains 4 red, 3 blue and 2 white balls. In how many ways can we select 3balls such that:

    a. They are all different color.

    b. They are all red.

    c. 2 are blue 1 is white.

    d. Exactly 2 are blue.

    e. None is white.
    Last edited by mr fantastic; March 27th 2009 at 07:55 PM. Reason: Moved to a new thread, re-formatted etc. etc.
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  2. #2
    MHF Contributor red_dog's Avatar
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    a) 4\cdot 3\cdot 2=24

    b) C_4^3=4

    c) C_3^2\cdot 2=6

    d) 2 blue, 1 red: C_3^2\cdot 4=12

    or 2 blue, 1 white: C_3^2\cdot 2=6

    12+6=18

    e) 3 red: C_4^3=4
    or 3 blue: C3^3=1
    or 2 red, 1 blue: C_4^2\cdot 3=18
    or 1 red, 2 blue: 4\cdot C_3^2=12
    4+1+18+12=34
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