Ice Cream Combinatorics > An ice cream store offers $14$ different flavors. Customers can purchase a single scoop or a double scoop ice cream. The double scoop portion **DOES NOT** allow two scoops of the same flavor. How many different ice creams can be purchased? I am not too sure how to do this problem. Do I just do $_{14}C_1$ (Single scoop) + $_{13}C_1$ (Double scoop)? Or is there a different way to tackle this problem?

You have the single scoops correct, but the double scoops would be $14\choose2$. Thus you have $14+{14\choose2}$ possibilities.