How many combinations of coins make 65 cents? - Answers

It gets to be a lot of work to find them all. I will show you how to do it without the pennies, then it will just take a bit of time to do the next step and do it with pennies if you want to use those too. Think about using 2 quarters, 1 quarter or no quarters. If you use 2 quarters, you have to make the remaining 15¢ with either no dimes or 1 dime and the rest has to be in nickels. That gives us 2 ways. If you use 1 quarter, you have to make the remaining 40¢ with either no dimes, 1 dime, 2 dimes, 3 dimes or 4 dimes and the rest, if there is any, has be to in nickels. That's 5 more ways. If you don't use any quarters, you have to make the entire 65¢ with either 0, 1, 2, 3, 4, 5 or 6 dimes and the rest in nickels. That's 7 more ways. 2+5+7 = 14 ways in all. Now go through the same process but add in pennies!