Statistics Help

Question

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

The back of the book says 6240, but I have no idea how they got that answer.

Answer 1

The tricky part is the number of ways (combinations) of choosing 2 DIFFERENT desserts from 13. It does not matter in what order the two desserts are picked. That number of combinations is
13!/(11!*2!) = (13*12)/2 = 78.

We are assuming that they are required to have two different desserts. Zero or one dessert is "not an option", as they say.

Now multiply that 78 by the possible number of main dishes (8) and the number of vegetable dishes (10). You will get the answer.