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Math Help - Dice

  1. #1
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    Dice

    What is the probability of throwing exactly two 3x a two and 2x a three with five normal dice? Order is not to be respected (eg 22233=32322)
    The possible combinations for n=6 and k=5, if order is to be neglected and repetition (as the task is about dice) is possible, is the formula (n+k-1 // k) which equals 720 possibilities. Thus the probability for axactly two threes and three twos is 1/720.
    The solution is 10 //7776 though. Where is my mistake?

    Thanks
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  2. #2
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    I disagree with your suggested answer. You must consider order.
    If we throw a die five times there are 6^5 different possible outcomes(5-tuples).
    Of those there are only 10 that contain exact two 3's and three 2's.
    So what is the probability?
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  3. #3
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    But why do you have do consider order when 33322 is the same as 32223 - I still dont get that. 6^5 possibilities would be right if there was a difference between e.g 21 an 12...
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  4. #4
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    Quote Originally Posted by Schdero View Post
    I still dont get that. 6^5 possibilities would be right if there was a difference between e.g 21 an 12...
    Once again: order must be considered.
    The pair (1,2) is different from the pair (2,1).
    If the question were, "what is the probability of tossing a one and a two?"
    The answer is \frac{2}{36} because there are two ways out of thirty-six to do it.

    From a content point of view there are only 21 different outcomes.
    But the difference is that all contents do not have the same probability.
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