Question

There are nine parking spaces next to each other in aparking lot. Nine cars need to parked by an attendant. Three of the cars aresports cars, three are large domestic cars, and three are imported compacts.Assuming the attendant parks the cars at random, what is the probability thatthe three sports cars are parked next to each other?

Answer 1

Answer:

The probability that 3 sports cars are parked together is 0.0833.

Step-by-step explanation:

An attendant has to park 9 cars.

He can park all the 9 cars i, 9! = 362880 ways.

If the attendant park the cars such that all three sports car are parked next to each other, then the number of ways to do this is:

Consider the 3 sports cars as 1 unit.

Then there are total 7 parking spaces, _, _, _, _, _, _, (SSS)

The three sports cars can be parked together in 3! = 6 ways.

The remaining 6 cars can be parked in 6! = 720 ways.

Compute the probability that 3 sports cars are parked together as follows:

$P(3\ sports\ cars\ together)=\frac{7\times6!\times3!}{9!}=\frac{7\times720\times6}{362880}= 0.0833$

Thus, the probability that 3 sports cars are parked together is 0.0833.