Jordan is planning to buy a vehicle. He has the following choices.

Question

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?
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.

Answer 1

Jordan's error lies in the way he is calculating the total number of possible vehicle choices. The correct approach to find the total number of combinations is to multiply the number of choices for each category, rather than adding them.

Jordan has:

• 2 choices for type (sedan or SUV)
• 2 choices for transmission (5-speed or automatic)
• 5 choices for color (red, blue, black, green, or silver)
• 2 choices for top (sunroof or no sunroof)

To find the total number of combinations, you would multiply the number of choices in each category:

Total choices = (Number of types) × (Number of transmissions) × (Number of colors) × (Number of tops)
Total choices = 2 × 2 × 5 × 2 = 40.

Therefore, Jordan's error is:

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