2004 AMC 10A Problem 12

Question

Henry’s Hamburger Heaven offers its hamburgers with the following condiments: ketchup, mustard, mayonnaise, tomato, lettuce, pickles, cheese, and onions. A customer can choose one, two, or three meat patties, and any collection of condiments. How many different kinds of hamburgers can be ordered?

24

256

768

40{,}320

120{,}960

Answer: C

Concepts:multiplication principle subsets

Difficulty rating: 1190

Small hint:

Each of the

8

condiments is independently included or left out

Big hint:

Multiply the

2^8

condiment choices by the

3

choices of patty count

Solution:

Each of the

8

condiments is independently in or out, giving

2^8 = 256

condiment combinations.

For each of these there are

3

choices of patty count, so the number of hamburgers is

3 \times 256 = 768.

Thus, the correct answer is C.