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discrete math problem

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i have a hw problem that i have problem solving. w + x+ y + z = 12 how many nonnegative interger solutions are there? well, using the "r-combinations w/ repitition allowed" rule u get 3 seperators so the answer would be C(12+3,12) -> C(15,12) ok, here''s what i have the problem in: w needs to be 0 <= w <= 4, meaning it can only be 0,1,2,3,or 4 0<=x<=5 0<=y<=8 0<=z<=9 having a hard time with this... please help

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nm, i got it.

and if any1 cares, this is how i did it.
total poss: C(15,12) = 455
subtract the ones outside each range for each variable
455-120-84-20-10
then since the subtracted #''s overlap by 4, u add 4
resulting in 225.

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