Question

In order to develop a more appealing​ cheeseburger, a franchise uses taste tests with 9 different​ buns, 8 different​ cheeses, 4 types of​ lettuce, and 3 types of tomatoes. If the taste tests were done at one restaurant by one tester who takes 10 minutes to eat each​ cheeseburger, approximately how long would it take the tester to eat all possible​ cheeseburgers?

Answer 1

8,640 minutes

Explanation:

Re-read the question: "How long would it take the test to eat all possible cheeseburgers?"

What are they asking for?

Answer: Total time test all possible burgers

We can break down the answer into a multiplication:

Total time to test all possible burgers =

Time to test each burger x Number of possible burgers

A) Time to test each burger is given - 10 minutes.

B) Number of possible burgers is essentially the total number of combinations of toppings you can have. The order of toppings doesn't matter, so this problem is called a "Combination Problem," as opposed to a "Permutation Problem" which is a problem when order matters.

How do we solve Combination problems?

Just multiply the quantity of each option.

Number of combinations of burger toppings = # bun types x # cheese types x # lettuce types x # tomato types

Number of combinations of burger toppings = 9 x 8 x 4 x 3 = 864

Now plug this into the original equation

Total time to test all possible burgers

= time to test each burger x number of possible burgers

= 10 minutes x 864 possible options

= 8,640 minutes