# number of solutions

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• Feb 17th 2010, 04:07 AM
CHAYNES
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 \$\displaystyle \binom{n+k-1}{k}\$ terms in the multinomial expansion of (x1+x1+.....+xn)^k
• Feb 17th 2010, 06:33 AM
Plato
Quote:

Originally Posted by CHAYNES
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 \$\displaystyle \binom{n+k-1}{k}\$ terms in the multinomial expansion of (x1+x1+.....+xn)^k

See my answer to #2.
For your part a) \$\displaystyle N=9~\&~K=4\$

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