# Solutions in non negative and positive intergers

• Mar 24th 2010, 09:42 AM
shmounal
Solutions in non negative and positive intergers
Hi, I've been going over some problems that I don't have answers too and just need some verification that what im doing is right!!

Find the number of solutions in a) non negative and b) positive intergers for $a+b+c+d=12$

For a) I have $\binom{12+4-1}{4-1} = \binom{15}{3} = 455$
and b) $\binom{8+4-1}{4-1} = \binom{11}{3} = 165$

I think/hope that is right but I've got no way of checking!! Cheers for any help!
• Mar 24th 2010, 10:00 AM
Plato
Quote:

Originally Posted by shmounal
Find the number of solutions in a) non negative and b) positive intergers for $a+b+c+d=12$

For a) I have $\binom{12+4-1}{4-1} = \binom{15}{3} = 455$
and b) $\binom{8+4-1}{4-1} = \binom{11}{3} = 165$

Both are correct.