Question

A fleet of nine taxis is to be dispatched to three airports in such a way that three go to airport a, five go to airport b, and one goes to airport
c. In how many distinct ways can this be accomplished?

Answer 1

A fleet of nine taxis is to be dispatched to three airports in such a way that three go to airport A, five go to airport B, and one goes to airport C. In how many distinct ways can this be accomplished?

2.44) Refer to Exercise 2.43. Assume that taxis are allocated to airports at random.

a) If exactly one of the taxis is in need of repair, what is the probability that it is dispatched to airport C?

b) If exactly three of the taxis are in need of repair, what is the probability that every airport receives one of the taxis requiring repairs?

So, my answer to 2.44a is 1/9. Hopefully this is correct at least :)

For 2.44b, my guess was

(3C1)(1/3)(2/3)2 * (5C1)(1/3)(2/3)4 * 1/3

The solutions manual on chegg (which seems to be riddled with errors) says something completely different. Is my calculation correct?

Answer 2

Answer:

There are 504 distinct ways can this be accomplished.

Step-by-step explanation:

A fleet of nine taxis is to be dispatched to three airports.

3 go to airport a, 5 go to airport b, and 1 goes to airport c.

The number of distinct ways this can this be accomplished is:

$(9C3)(6C5)(1C1)$

= $(84)(6)(1)(1)$

= 504

Therefore, there are 504 distinct ways can this be accomplished.