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Math Help - Multinomial distribution

  1. #1
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    Exclamation Multinomial distribution

    If five balanced dice are rolled, what is the probability that the number 1 and the number 4 will appear the same number of times?

    I know that n=5, but I can't figure out what other numbers to plug into the equation. 1 can appear once and 4 can appear once, or 1 can appear twice and 4 can appear twice. Anyone know how to do this??? The answer in the book is (2424)/(6^5)

    Thanks in advance!!
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  2. #2
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    So this includes the occurance that of the 5 dice.

    both #1 and #4 appear once together
    both #1 and #4 appear twice together
    both #1 and #4 appear not at all

    Can you think of any other ways?
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  3. #3
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    No I cannot think of any other ways. And I don't know how to solve for the probability still
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  4. #4
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    The number of ways:
    • zero times 4^5
    • one time (5)(4)(4^3)
    • two times \binom{5}{2}\binom{3}{2}(4)


    Now divide by 6^5
    Last edited by Plato; December 9th 2010 at 10:10 AM.
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  5. #5
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    That makes sense but does not give me the answer in the back of the book of 2424/(6^5)
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    Never mind, I figured it out. That 3 should be a 2 above
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  7. #7
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    Quote Originally Posted by holly123 View Post
    That makes sense but does not give me the answer in the back of the book of 2424/(6^5)
    I get the same as your text book: 2424
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