Question

of the 16 cars on a rental car lot, 6 are minivans, 7 are sedans, and 3 are hatchbacks. Thalia will rent 3 of these cars, chosen at random. What is the probability that Thalia will rent 1 of each of the 3 types of cars

Answer 1

The probability that Thalia will rent 1 of each of the 3 types of cars is; 9/40

Permutations

We are given;

• Total Cars = 16

• Minivans = 6

• Sedans = 7

• Hatchbacks = 3

Probability of choosing without replacement;

P(Minivans) = 6/16 = 3/8

P(Sedans) = 7/15

P(Hatchbacks) = 3/14

Thus;

Probabilities of picking each together = 3/8 * 7/15 * 3/14

Probabilities of picking each together = 3/80

Now, since thalia will rent 3 of the cars chosen at random, then possible permutations = 3! = 6

Thus, probability that Thalia will rent 1 of each of the 3 types of cars is;

P(rent one of 3 cars) = 6 * 3/80 = 9/40

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