Help understanding this homework problem

[hopesfall]

Ok so I'm trying to understand what I need to do for this homework problem and I can't seem to grasp it. This is what it says:


Let c(n) be the number of different groups of integers that can be chosen from the integers 1 through n- 1 so that the integers n each group add up to n (for example, 4= 1 + 1 + 1 + 1 = 1+ 1 + 2= 2 +2 .....). Write recursive definitions for c(n) under the following variations:

a You count permutations. Foe example, 1, 2, 1 and 1, 1, 2 are two groups that each add up to 4.

b. You ignore permutations.


Can anyone explain this problem to me in a simpler way? What's the best way to approach making a program like this?

Thanks in advance