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

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

I got 1/9 as my answer . Using multinomial coefficients


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?

I got 15/504 .

Are these answers right?

Answer 1

do for a) i did \[\left(\begin{matrix}8 \\ 3\hspace{2mm}5\hspace{2mm} 0\end{matrix}\right) =\frac{8!}{3!5!0!}=56\] and then this over the total number of ways = 504 ( obtained the same way but 9! instead of 9