Suppose you are looking for a new car and have narrowed down your decision down to a Mustang, but can’t decide on the exact color, transmission, engine, or options package. There are three sizes of engine (3.0 liters, 3.8 liters, and 4.6 liters), two transmissions (standard and automatic), five colors you like (black, silver, red, yellow, and green), and three option packages (GL, Sport, and XL). With all these possible choices, you want to know how many different Mustangs there are from which you must choose.

How many different Mustangs are possible?
a.
90 different Mustangs
b.
13 different Mustangs
c.
30 different Mustangs
d.
45 different Mustangs

Respuesta :

We are given several choices with the corresponding number of possible options for each choice. First, we have to choose between 3 engine sizes, then 2 transmissions, 5 colors, three option packages. To determine how many possible combinations of a Mustang is there to choose from, multiply all options:

3 engines * 2 transmissions * 5 colors * 3 option packages = 90 different Mustangs

Rule of product gives number of ways we can do a set of tasks. The total number of Mustangs possible is: Option a: 90 different Mustangs

What is the rule of product in combinatorics?

If a work A can be done in p ways, and another work B can be done in q ways, then both A and B can be done in [tex]p \times q[/tex] ways.

Remember that this count doesn't differentiate between order of doing A first or B first then doing other work after the first work.

Thus, doing A then B is considered same as doing B then A

Since it is given that:

  • Number of choices for engine: 3
  • Number of choices for transmissions: 2
  • Number of choices for colors: 5
  • Number of option packages: 3

For each of one task, the other task can be done their number of times, and then for each of their pair, the third can be done its number of times. And so on for fourth choice.

Using rule of product:

Total ways of choosing Mustangs = [tex]3 \times 5 \times 2 \times 3 = 90[/tex]

Thus,

The total number of Mustangs possible is: Option a: 90 different Mustangs

Learn more about rule of product here:

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