We can't use pennies at all, because if we used 5 pennies,
we would have to make the remaining 45 cents with only
1 or 2 coins, which is impossible.

So we can use either 0, 1 or 2 quarters.

1. Suppose we don't use any quarters.

Then we have to use at least 3 dimes because if we used 
only 2 dimes, we'd have to make the remaining 30 cents 
with 6 nickels, giving us 8 coins, which is not allowed. 

So we can use 3, 4, or 5 dimes, with the rest, if any, in nickels.  
That's 3 ways.

2. Suppose we use 1 quarter.

Then we don't necessarily have to use any dimes, because 
we can make the remaining 25 cents with 5 nickels, giving 
us only 6 coins. So we can use 0, 1, or 2 dimes with the 
rest in nickels.
That's 3 ways.

3. If we use 2 quarters, that's the whole 50 cents.
That's 1 way.

So that's a total of 3+3+1, or 7 ways.

Half dollars are not in circulation anymore. But if
we count having 1 half dollar, then the answer is 8.

Here are all the ways, not counting the case of 1 half dollar.

1.  0 quarters, 3 dimes, and 4 nickels.
2.  0 quarters, 4 dimes, and 2 nickels.
3.  0 quarters, 5 dimes, and 0 nickels.
4.  1 quarter,  0 dimes, and 5 nickels.
5.  1 quarter,  1 dime,  and 3 nickels.
6.  1 quarter,  2 dimes, and 1 nickel.
7.  2 quarters, 0 dimes, and 0 nickels.

Edwin