Question

A buyer of a new sedan can custom order the car by choosing from 5 different exterior colors, 3 different interior colors, 2 sound systems, 3 motor designs, and either manual or automatic transmission. How many choices does the buyer have?

Answer 1

A buyer of a new Sedan car custom order the car by choosing from 5 different exterior colors, 3 different interior colors, 2 sound systems, 3 motor designs and one of manual or automatic transmissions.

That is, the exterior color of the car can be chosen in “5” different ways.

The interior color of the car can be chosen in “3” different ways.

The sound system of the car can be chosen in “2” different ways.

The motor design of the car can be chosen in “3” different ways.

The transmissions of the car can be chosen in “2” different ways.

As more than 1 selections has to be made, Multiplication Principle of counting will be used.

 

Consider the Multiplication Principle,

“If one event can occur in m ways and a second event can occur in n ways after the first event has occurred, then two events can occur in m × n ways.”

 

Using the multiplication principle, the number of choices a buyer has,

5 × 3 × 2 × 3 × 2 = 180

Using the multiplication principle, the number of choices a buyer has,

5 × 3 × 2 × 3 × 2 = 180