Suppose there is a 0.20 coin instead of 0.25 how many ways can you give me a dollar if you are only allowed to use nickels (0.05), dimes (0.10), and 0.20 coins?

There are multiple ways:

1) I would give you a 20 cent coin five times.
2)I would give you 10 dimes 
3)I would give you 20 nickels 
4)I would give you 5 dimes and 10 nickels
5)I would give you 10 nickels, a 20 cent and 2 dimes
6)I would give you 2 dimes, two 20 cent coins, and eight nickels

Those are a few I could think of atm. Let me know if you need some more. 

Hope this helped :)