Janice was given a piggy bank on her seventh birthday, and she put it to use immediately. Each time she puts one or more coins into the piggy bank, she keeps track of the number of coins she has collected to date and the accumulated value of her collection. Janice collects only nickels, dimes, and quarters. Six months after her seventh birthday, Janice looked at her record and ascertained that she had collected 960 coins, which were worth $72. How many combinations of coins are possible in Janice's collection?