If we don't use a half dollar or any quarters, we can use from
0 through 5 dimes, inclusive, and the rest, if any, in nickels.
That's 6 ways.

If we don't use a half dollar and use 1 quarter, we can use 0, 1 or
2 dimes and the rest in nickels.
That's 3 ways.

There are only 2 more ways, either 2 quarters or 1 half dollar.
That's 2 ways.

Total: 6 + 3 + 2 = 11 ways.

Edwin