Probability of selecting two trucks An automobile manufacturing plant produced $31$ vehicles today: $11$ were sedans, $11$ were vans, and $9$ were trucks. Plant managers are going to choose two of these vehicles for a thorough inspection. The first vehicle will be chosen at random, and then the second vehicle will be chosen at random from the remaining vehicles. What is the probability that two trucks will be selected?

There are

$\frac{31*30}{2}=465$

possibilities to choose 2 vehicles out of the 31, and

$\frac{9*8}{2}=36$ , such that two trucks are selected,

so the probability is

$\frac{36}{465}=\frac{12}{155}$.

The other way to calculate it :

At the first step, the probability if $\frac{9}{31}$ to choose a truck, at the second step it is $\frac{8}{30}$ (if in the first step,a truck was chosen), so the probability of choosing two trucks is $\frac{9}{31}*\frac{8}{30}=\frac{12}{155}$.