Final answer:
The question is about calculating the probability that each of the three airports receives one taxi that needs repair. One taxi goes to airport A, one to airport B, and one to airport C. The correct probability is found through careful selection of taxis and is 1/21.
Step-by-step explanation:
The question asks for the probability that every airport receives one taxi that is in need of repair, given a fleet of nine taxis dispatched to three airports with three taxis going to airport A, five to airport B, and one to airport C, and exactly three taxis needing repairs. To find the probability:
- Count the ways to choose one taxi for each airport that needs repair: (3 choose 1) for airport A, (5 choose 1) for airport B, and there's only one taxi for airport C, so (1 choose 1).
- Calculate the individual probabilities: for airport A that's 3/9, for airport B that's 5/9, and for airport C, since there's only 1 taxi, it's 1/9.
- Multiply these together: (3/9) * (5/9) * (1/9).
- Since the taxis are chosen without replacement, adjust the probabilities for subsequent choices: the second probability becomes 5/8 and the third 1/7.
- Multiply the adjusted probabilities: (3/9) * (5/8) * (1/7).
- Simplify this to find the probability, which is 1/21.
The correct answer is option B) 1/21.