SOLUTION: In his pocket, Tamir has fewer than 10 coins totaling 75 cents. How many possible combinations of coins could he have?

There are 17 ways to have 75 cents in coins if you allow half dollars,
11 if you don't.

 1.  6 dimes, 3 nickels.
 2.  7 dimes, 1 nickel.
 3.  1 quarter, 2 dimes, 6 nickels.
 4.  1 quarter, 3 dimes, 4 nickels.
 5.  1 quarter, 4 dimes, 2 nickels.
 6.  1 quarter, 5 dimes.
 7.  2 quarters, 5 nickels.
 8.  2 quarters, 1 dime, 3 nickels.
 9.  2 quarters, 2 dimes, 5 pennies.
10.  2 quarters, 2 dimes, 1 nickel.
11.  3 quarters.
12.  1 half dollar, 5 nickels.
13.  1 half dollar, 1 dime, 2 nickels, 5 pennies.
14.  1 half dollar, 1 dime, 3 nickels.
15.  1 half dollar, 2 dimes, 5 pennies.
16.  1 half dollar, 2 dimes, 1 nickel.
17.  1 half dollar, 1 quarter.

Edwin