Question

An exam has 12 problems. How many ways can (integer) points be assigned to the problems if the total of the points is 100 and each problem is worth at least 5 points?

Answer 1

In other words I think they are asking how many ways can the leftover 40 points (since each has to be 5 so 5*12=60) can be assigned to the questions

Answer 2

I think the answer is C(40+12-1,12-1)=c(51,11) but I don't quite understand why they minus 1

Answer 3

but can't it also be 51!/40!?

Answer 4

i think it is what you said

Answer 5

12 boxes in which to put 40 points

Answer 6

But how would I do that? do you understand why they subtracted 1? or is that not the correct way to do it

Answer 7

for 12 boxes you only need 11 dividers

Answer 8

for example if you had 3 boxes and one item (call it x) was can put it in the 3 boxxes as follows

x||
|x|
||x

Answer 9

that make sense now!! thanks!