I am working on a scheduling algorithm for teachers taking classes, and I am working out possible run times. I have simplified the problem down to this analogy
If I had 18 boxes and 42 marbles. Each box could hold from 0 - 42 marbles. The amount of combinations would be $42^{18} = 165381614442044595841154678784 = 1.653816144 \times 10^{29}$ right?
however my problem is i have 18 boxes and 42 marbles each box can hold from 0-6 marbles how do I work out how many combinations?
if it helps the actual problem is i have 18 teachers and 42 classes that need to be taught. classes do not overlap. each teacher can only take 6 classes
– Aleddd Apr 16 '15 at 00:01i dont really under stand how that would change the answer .. 2 boxes, 1 marble ..
combinations would be ? .. box1 - 1marble .. box2 - 0marble .. or .. box1 - 0marble .. box2 - 1marble ..
2 combinations as the marble has to be in one box?
– Aleddd Apr 16 '15 at 00:06