Question

Sally is interested in buying a car. If she has a choice of 3 colours (red, green or blue), two body types (two or four doors), and 3 engine types (four, six or eight cylinders), calculate how many different models she can choose from.
A) 6
B) 8
C) 12
D) 16
E) 18

Answer 1

Hint:
We will use the fundamental principle of counting to solve this question. The fundamental principle of counting states that if there are p ways to perform an action and q ways to perform other actions, then to do both of them, there are p$ \times $q ways. Here, Sally has p ways to choose between colours, q ways to choose between body types and r ways to choose between the engine types, then there are total p$ \times $q$ \times $r ways that she can choose from.

Complete step by step solution:
We are given that Sally wants to buy a car.
She has a choice between 3 colours (red, green or blue),
She has a choice between two body types (two or four doors), and
She has a choice between 3 engine types (four, six or eight cylinders).
We need to calculate the number of various models of car from which she can choose from.
We will use the fundamental principle of counting here.
Statement: The fundamental principle of counting states that if there are p ways to perform an action and q ways to perform other actions, then to do both of them, there are p$ \times $q ways.
Or in other simpler words, the fundamental principle of counting is a way to figure out the number of outcomes by multiplying the possibility of the events together to reach a total number of outcomes.
Here, let Sally has p ways to choose between colours, q ways to choose between body types and r ways to choose between the engine types, then there are total p$ \times $q$ \times $r ways that she can choose from i.e., p = 3, q = 2, r = 3, therefore,
The total choices Sally has: p$ \times $q$ \times $r = 3$ \times $2$ \times $3 = 18.

Therefore, option (E) is correct.

Note:
Another way of choosing items in mathematics is combinations. If we have to choose r items out of n items then we use combinations. it is represented by ${}^{n}{C_{r}}$ and it’s formula is $\dfrac{n!}{r!(n-r)!}$