If we don't use any quarters, we can use 0,1,2,3,4, or 5 dimes
and the rest of the 50 cents, if any, in nickels. That's 6 ways.
If we use 1 quarter, then we can use 0,1, or 2 dimes, and
the rest in nickels. That's 3 more ways.
We can use 2 quarters. That's 1 more way.
So altogether there are 6+3+1 or 10 ways.
I'll list them:
1. 10 nickels.
2. 1 dime and 8 nickels.
3. 2 dimes and 6 nickels.
4. 3 dimes and 4 nickels.
5. 4 dimes and 2 nickels.
6. 5 dimes.
7. 1 quarter and 5 nickels.
8. 1 quarter, 1 dime, and 3 nickels.
9. 1 quarter, 2 dimes, and 1 nickel.
10. 2 quarters.
Edwin
