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Math Help - number of solutions

  1. #1
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    number of solutions

    Hey there was wondering if anyone could give me some help with these questions or show me a link were i could get some information to help solve them.

    a) How many solutions in non-negative integers are
    there to the equation:
    w + x + y + z = 9 ?

    b) How many solutions in positive integers?

    c) Use multisets to show that there are \binom{n+k-1}{k} terms in the multinomial expansion of (x1+x1+.....+xn)^k
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  2. #2
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    Quote Originally Posted by CHAYNES View Post
    Hey there was wondering if anyone could give me some help with these questions or show me a link were i could get some information to help solve them.

    a) How many solutions in non-negative integers are
    there to the equation:
    w + x + y + z = 9 ?

    b) How many solutions in positive integers?

    c) Use multisets to show that there are \binom{n+k-1}{k} terms in the multinomial expansion of (x1+x1+.....+xn)^k
    See my answer to #2.
    For your part a) N=9~\&~K=4

    For your part b) N=5~\&~K=4, because we have already used 4 ones. Giving each one to start with.
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