Question

The Carson family will purchase three used cars. There are two models of cars available, Model A and Model B, each of which is available in four colors: blue, black, red, and green. How many different combinations of three cars can the Carsons select if all the cars are to be different colors?
A. 24
B. 32
C. 48
D. 60
E. 192

Answer 1

32 different combinations of three cars can the Carsons select if all the cars are to be different colors.

B. 32

Explanation:

As it is given there are four available colours of the car. That means we have 4 cars. $2 \times 4 =8$. Now choose the first car. The no.of way of choosing the first car is equalled to 8 and imagine the first car Colour is black. Now we have a black car so we have to choose from 6 options apart from black.

Now no.of way of choosing the 2 car = 6 and imagine it is blue. Now we have to choose two colour car, so now we have 4 options to choose from. The no.of choosing the car = 4. Now let's calculate the total arrangement - $8 \times 6 \times 4=192$. It is the total calculation for three cars.

But we have to know the selection so three cars can also be arranged in 6 ways. So the number of different combinations of three cars can be calculated as 192÷6= 32. This is how the selection is being done.