EXAMPLE 1.4.12 Gomer is considering the purchase of a new super-cheap sport/utility vehicle, the Skuzuzi Kamikaze. He must choose a vehicle, taking into account the following options:

i. Transmission: 4-speed standard transmission, 5-speed standard transmission, or automatic transmission;

ii. Bumper: steel bumpers, vinyl bumpers or 2x4 boards bolted to the front and back;

iii. Top: hard-top, vinyl top convertible, or chicken wire stapled over the roll bar;

iv. Funerary accessory: complementary funeral wreath or cremation urn.

How many different vehicle option packages are possible?

SOLUTION

Gomer must make four decisions.

i. Transmission: 3 options.
ii. Bumper: 3 options.
iii. Top: 3 options;
iv. Funerary accessory: 2 options.

According to the Fundamental Counting Principle, the number of outcomes is
(3)(3)(3)(2) = 54.

In other words, if the dealership wanted to make sure that they had at least one model for each possible configuration, they would need at least 54 cars.