# number of solutions

• 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 $\binom{n+k-1}{k}$ 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 $\binom{n+k-1}{k}$ terms in the multinomial expansion of (x1+x1+.....+xn)^k

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.