Question

jordan is planning to buy a vehicle. he has the following choices.
type: sedan or suv
transmission: 5 - speed or automatic
color: red, blue, black, green, or silver
top: sunroof or no sunroof
jordan says that he has a total of 2 + 2 + 5 + 2, or 11, possible vehicle choices. what is jordan’s error?
options:

• he should have multiplied the sum by 4.
• he should have added only the choices for type and transmission.
• he should have multiplied only the choices for type and transmission.
• he should have multiplied the choices, instead of adding them.

Explanation:

To find the total number of possible vehicle choices, we use the fundamental counting principle, which states that if there are \( n_1 \) ways to do the first task, \( n_2 \) ways to do the second task, \( n_3 \) ways to do the third task, and \( n_4 \) ways to do the fourth task, then the total number of ways to do all four tasks together is \( n_1\times n_2\times n_3\times n_4 \).

• For the type (sedan or SUV), there are \( 2 \) choices.
• For the transmission (5 - speed or automatic), there are \( 2 \) choices.
• For the color (red, blue, black, green, or silver), there are \( 5 \) choices.
• For the top (sunroof or no sunroof), there are \( 2 \) choices.

The correct total number of possible vehicle choices is \( 2\times2\times5\times2 = 40 \). Jordan added the number of choices for each category (\( 2 + 2+5 + 2=11 \)) instead of multiplying them. So his error was that he should have multiplied the choices, instead of adding them.

Answer:

He should have multiplied the choices, instead of adding them.