1. The problem statement, all variables and given/known data How many solutions are there to the equation where xn is non negative. x1+x2+x3+x4+x5=30 where x1,x2,x3,x4,x5<8? 2. Relevant equations 3. The attempt at a solution well I thought the only way to ensure this is when the first 7 'dots' are placed, since if all the 'dots' are placed in let's say x1 then by the 8th dot it could also be arranged in x1, hence not satisfying the condition. ie C(11,4) ... but the sltn says C(9,4). which I thought was strange; doesn't that sltn imply that xn can ≥8 when the first 5 dots are arranged? and the only condition on xn is that they are non negative... so they can be zero.