Statistics, permutations and combinations

Question

Space Shuttle Menu     Space shuttle astronauts each consume and average of 3000 calories per day. One meal normally consists of a main dish, a vegetable dish, and two different desserts. The astronauts can choose from 10 main dishes, 8 vegetable dishes, and 13 desserts. How many different meals are possible?

Answer 1

Since they must choose 2 out of 13 desserts, there are (13)(12)/2=78 choices of two desserts.

The total number of different meals is therefore 10×8×78=6240.