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Math Help - ball throwing question..

  1. #1
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    ball throwing question..

    i have 6 balls .
    balls 1-3 are white
    balls 4,5 are red
    ball 6 is blue

    we throw these balls into 5 holes numerated 1-5
    what is the probability that in hole number 3 we get only red balls
    and there is no red balls in the other holes

    i saw another student soluton and it says
    \frac{1^24^4}{5^6}

    cant understand the numerator
    we need to choose 1 red ball out of 2 for hole number 3,so its \binom{2}{1}

    divided by 5^6

    am i correct?
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  2. #2
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    Re: ball throwing question..

    Quote Originally Posted by transgalactic View Post
    i have 6 balls .
    balls 1-3 are white, balls 4,5 are red, ball 6 is blue
    we throw these balls into 5 holes numerated 1-5
    what is the probability that in hole number 3 we get only red balls
    and there is no red balls in the other holes
    i saw another student soluton and it says
    \frac{1^24^4}{5^6} cant understand the numerator
    That answer assumes a function model.
    There are 5^6 functions from a set of six to a set of five.
    There is one way to put the balls 4&5 into hole #3.
    There are 4^4 ways to put the other balls into the other holes.
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  3. #3
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    Re: ball throwing question..

    i forgot to mention that every hole can contain at most 6 balls
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  4. #4
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    Re: ball throwing question..

    Quote Originally Posted by transgalactic View Post
    i forgot to mention that every hole can contain at most 6 balls
    That fact does not change the answer in any way.
    All six balls can be in the same hole.
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