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Math Help - Permutations/Combinations

  1. #1
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    Permutations/Combinations

    Hello,

    I would like some guidance or help with questions b and c below please. Any assistence will be appreciate. Thanks in advance!

    a. In how many ways can 6 people be lined up to get on a bus?
    My answer: 6!, or put another way, 6 * 5 * 4 * 3 * 2 * 1 = 720 ways.

    b. If 3 specific persons, among 6, insist on following each other, how many ways are possible?
    c. If 2 specific persons, among 6, refuse to follow each other, how many ways are possible?
    Last edited by sparky; February 8th 2009 at 02:12 PM. Reason: Correct a mistake
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  2. #2
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    b. Tie the 3 specific people together. We can arrange them in 6 different ways. But we can also arrange them all in 24 different ways.

    24*6=144 ways

    c. tie the two people together and we can arrange them in 2 ways. We can arrange them all in 5! or 120 ways.

    120*2=240.

    But they DO NOT want to be together: 720-240=480 ways.
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  3. #3
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    Thank you for your reply galactus!

    How did you get 24 in your workings for question b?

    I tied the three people together as you suggested (A, B and C) and I got 42. Here is my logic and working below. Tell me where I went wrong:

    1. 2. 3. 4.
    A D D D
    B A E E
    C B A F
    D C B A
    E E C B
    F F F C

    1.
    A, B & C = 3!
    D, E & F = 3!
    Sub total = 12 possible ways

    2.
    A,B & C = 3!
    D = 1!
    E & F = 2!
    Sub total = 9 possible ways

    3.
    A, B & C = 3!
    D & E = 2!
    F = 1!
    Subtotal = 9 possible ways

    4.
    A, B & C = 3!
    D, E & F = 3!
    Subtotal = 12 possible ways

    Grand total: 42 possible ways
    Last edited by sparky; February 6th 2009 at 04:27 PM. Reason: correct a mistake
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  4. #4
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    Regarding question C, I got 208. Here is my logic and workings. Let me know where I went wrong. Thanks again.

    1 2 3 4
    A A A A
    C C C C
    B D D D
    D B E E
    E E B F
    F F F B

    5 6 7 8
    B B B B
    C C C C
    A D D D
    D A E E
    E E A F
    F F F A

    1 - 4 =
    4! + 4! + 4! + 4! + 1! + 1! + 1! + 1! + 1! + 1! + 1! + 1! = 104 possible ways

    plus
    5 - 8 =

    4! + 4! + 4! + 4! + 1! + 1! + 1! + 1! + 1! + 1! + 1! + 1! = 104 possible ways

    Grand total = 208 possible ways
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