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Combinatorics

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Pick a Car Lot with the Most Options: Counting Principles

COMBIN-GDOBIK

My buddy is a car salesman and he has a very picky customer. He needs to choose which car lot to take the customer to. The customer is open to buying either a car or a truck, but he wants as many options as possible. My friend wants to take the customer to the car lot with the most options. Here are the car lots in a five mile radius:

  1. Car Lot A has 30 different brands of cars and each car brand has 4 different models.

  2. Car Lot B has 15 different brands of cars and each car brand has 5 different models. Customers can choose a manual transmission or an automatic transmission for the car they buy.

  3. Car Lot C has both trucks and cars. Each of their 23 brands has 2 models of trucks and 4 models of cars.

  4. Car Lot D has 6 brands of trucks, each with 3 models. They also have 14 brands of cars, each with 4 models. Customers can choose a manual transmission or an automatic transmission for the car they buy.

Which car lot do you recommend to your friend?

A

Car Lot A

B

Car Lot B

C

Car Lot C

D

Car Lot D