To have the most coins we must have as many pennies as possible.
But we must have at least one each of quarters, dimes and nickels.
So we get just 1 each of those. 1 quarter, 1 dime, and 1 nickel
makes 40 cents, so we need 60 pennies to make $1.  Therefore the 
most possible number of coins is 63:

1 quarter, 1 dime, 1 nickle and 60 pennies, which is 63 coins.

To have the least number of coins we must have as few pennies as
possible, which is 5. We must have as many quarters as possible, 
which is of course 3. So that accounts for 80 cents.  Now we
must get the remaining 20 cents in dimes and nickles.  That
can only be 1 dime and 2 nickels, since we can't use 2 dimes
and no nickles.  Therefore the least possible number of coins is 11:

3 quarters, 1 dime, 2 nickles and 5 pennies, which is 11 coins.

Edwin