At a restaurant, customers can choose up to four side dishes and up to two main courses. If a customer must have at least 1 side dish and 1 main course, how many distinct dinner plate combinations are possible?
The answer is 45. I can only calculate 12.
Call the four side dishes A,B,C,D.
Call the Main courses E and F.
E goes with A,B,C,D.
F goes with A,B,C,D.
8 current.
Now EF goes with A,B,C,D.
12 total.
Best Answer
If any number of side dishes are allowed, then you may note that there are in total $2^4 - 1 = 15$ combinations of side dishes and $2^2 - 1 = 3$ combinations of main dishes, so a total of $15 \cdot 3 = 45$ total combinations.