how many different sums of money can you make with a penny, a dime, a one-dollar coin, and a two-dollar coin?

Answer 1

One, because if you add them up in different order you're still going to get the same answer.(if I understood the question correctly)

Answer 2

well the answer in the textbook is 15? :S i don't know, it's in the unit of combinations and the binomial theorem

Answer 3

2^n-1=2^4-1=15

2 is always the base (you either pick it or you don't) and 4 because there are 4 options and subtract one because you exclude the empty or null set.