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:
[tex]P(3\ sports\ cars\ together)=\frac{7\times6!\times3!}{9!}=\frac{7\times720\times6}{362880}= 0.0833[/tex]
Thus, the probability that 3 sports cars are parked together is 0.0833.
