Q. You go to a bakery to select some baked goods for a dinner party. You need to choose a total of 12 items. The baker has seven different types of items from which to choose, with lots of each type available. How many different boxfuls of 12 items are possible for you to choose?
A. ${7+12−1\choose 12} = 18,564 \ \text{boxes}$
I've been trying for an hour, but I absolutely don't understand how to answer this question. I couldn't even figure it out looking at the given answer.
The question asks $\sum_{i=1}^{7} x_i = 12$ where $x_i$ are number of different types of items. We have $x_i \ge 0$, so use stars and bars to get $\binom{7+12-1}{12}$.