posted by Tlyer M .
I Have 5 coins: a penny, a dime, a nickel, a quarter, a loonie. How many different amounts of money could I pay using any combinations of these coins?
I can use the penny in 2 ways, either take it or not take it.
I can use the dime in 2 ways, either take it or not take it.
So the number of ways is
2x2x2x2x2 = 32
but that would include the case of not taking any of the coins, and we want to have at least some kind of value
so the number of ways is 32-1 = 31