How many combinations of quarters dimes and nickels equal 95 cents?

Answer 1

There are 11 combinations. Beginning with the largest coin, they are:

1) 3 quarters, 1 dime, and 2 nickels

2) 2 quarters, 4 dimes, 1 nickel

3) 2 quarters, 3 dimes, 3 nickels

4) 2 quarters, 2 dimes, 5 nickels

5) 2 quarters, 1 dime, 7 nickels

6) 1 quarter, 6 dimes, 2 nickels

7) 1 quarter, 5 dimes, 4 nickels

8) 1 quarter, 4 dimes, 6 nickels

9) 1 quarter, 3 dimes, 8 nickels

10) 1 quarter, 2 dimes, 10 nickels

11) 1 quarter, 1 dime, 12 nickels

If you do not need to use all three coins, there are 15 more combinations:

12) 3 quarters, 2 dimes

13) 3 quarters, 4 nickels

14) 2 quarters, 9 nickels

15) 1 quarter, 7 dimes

16) 1 quarter, 14 nickels

17) 9 dimes, 1 nickel

18) 8 dimes, 3 nickels

19) 7 dimes, 5 nickels

20) 6 dimes, 7 nickels

21) 5 dimes, 9 nickels

22) 4 dimes, 11 nickels

23) 3 dimes, 13 nickels

24) 2 dimes, 15 nickels

25) 1 dime, 17 nickels

26) 19 nickels