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

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.

2004 AMC 10A Problem 12

Answer: C

Difficulty rating: 1190

Solution:

Problem 12 in Other Years