Question 34975
My solution is much longer, but same answer. 

I read this problem as saying, "How many ways can you make a hamburger with five different fixings?" This means I can make a hamburger with all five fixings, or as little as none--just a plain burger with a bun. 

Five Fixings: 1 way
Four Fixings: 5C4 = 5 ways
Three Fixings: 5C3 = 10 ways
Two Fixings: 5C2 = 10 ways
One Fixing: 5 ways
Zero Fixings: 1 way


1+5+10+10+5+1 = 32

32 ways to make a hamburger when there are five fixings to choose from, and amount of the five chosen vary.