SOLUTION: how many combinations of only quarters nickels and dimes can go into 85cents

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Question 306551: how many combinations of only quarters nickels and dimes can go into 85cents
Answer by solver91311(24713) (Show Source):
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If you have zero quarters, then you can have:

0 dimes and 17 nickels
1 and 15
2 and 13
3 and 11
4 and 9
5 and 7
6 and 5
7 and 3
8 and 1

If you have one quarter, then you can have

0 dimes and 12 nickels
1 and 10
2 and 8
3 and 6
4 and 4
5 and 2
6 and 0

If you have two quarters, then you can have

0 dimes and 7 nickels
1 and 5
2 and 3
3 and 1

If you have three quarters, then you can have

0 dimes and 2 nickels
1 dime and 0 nickels

So, if having zero of any denomination of coin is allowed, you have 21 possibilities.

If you must have at least one of each denomination of coin, then you have 8 possibilities

If you have one quarter, then you can have

1 dime and 10 nickels
2 and 8
3 and 6
4 and 4
5 and 2

If you have two quarters, then you can have

1 dime and 5 nickels
2 and 3
3 and 1

John