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Math Help - yahtzee problem! due in 9 hours!

  1. #1
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    yahtzee problem! due in 9 hours!

    the problem is the following:

    In the game of Yahtzee (or Yacht), five dice are thrown. Show that the probability of throwing a large straight (5 numbers in a row, the order does not matter) is 5/162 .
    Alternatively, you may solve the following, harder, problem. Show that the probability of throwing a small straight (4 numbers in a row) is 10/81 . Do not count small straights which are also large straights.

    so i did the first part as follows :
    the 5 numbers in a row can be wether 65432 or 54321 thus the chances to get them will be : 2(5*4*3*2*1)/6^5 but i don't really know how to represent my answer in a professional way !! for the second one, i got no clue how to do it !!

    ps: we throuw the dices only once not like in the real game when we throw them twice (i think).
    thank you for your very needed help
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  2. #2
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    Quote Originally Posted by yaszine View Post
    the problem is the following:

    In the game of Yahtzee (or Yacht), five dice are thrown. Show that the probability of throwing a large straight (5 numbers in a row, the order does not matter) is 5/162 .
    Alternatively, you may solve the following, harder, problem. Show that the probability of throwing a small straight (4 numbers in a row) is 10/81 . Do not count small straights which are also large straights.
    Divide thy problems into two problems.

    1)You get 1,2,3,4,5
    2)You get 2,3,4,5,6

    Without loss of generality the probability is the same in both problems.

    If you are trying to get: 1,2,3,4,5.
    So the probablity in that order is,
    (1/6)(1/6)(1/6)(1/6)(1/6)
    Multipled by the number of ways you can get these arrangements which is 5!
    Thus,
    \frac{5!}{6^5}=\frac{120}{7776}=\frac{5}{324}

    Now the probablity of: 2,3,4,5,6
    Is too \frac{5}{324}

    Thus, the total probability is,
    \frac{5}{324}+\frac{5}{324}=\frac{5}{162}
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