# Math Help - Solutions in non negative and positive intergers

1. ## 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!

2. 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.