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