Steve has one quarter, two nickels and three pennies. Assuming no items are free, for how many different-priced items could Steve individually pay for with exact change?

Steve can use no quarters or one quarter, for two possibilities.

Steve can use 0, 1, or 2 nickels, for three possibilities.

And Steve can use 0, 1, 2, or 3 pennies, for four possibilities. That gives possible combinations. But we must remove the combination where Steve does not use any coins, leaving us with

Note that this only works because each obtainable value can only be obtained in 1 way. In other words, if there were 5 pennies instead of 3, there would be there would be 2 ways to buy something that costs 5 cents: 1 nickel or 5 pennies.