There isn't really enough information in the question. A reasonable way to fill in the gaps in a precise manner would be as follows.
Five people get into an elevator on the ground floor. Each person is equally likely to want to go to any other floor, independently of the other people. Given that at least one person wants each of floors $2$, $3$ and $4$, and no-one wants any other floor, what is the probability that exactly two people want floor $3$?
(It might be that the intended interpretation was "at least two" rather than "exactly two".)
We can put the people in order, and write down the sequence of floors they want to go to. A sequence might be $3,2,2,4,2$ or $2,3,4,2,3$ (order matters).
We have two questions to solve: how many possible sequences are there, and how many of these have exactly two $3$s? Then the second number divided by the first gives the probability, since all sequences are equally likely.
Hint for the first: there are $3^5$ sequences using only $2$s, $3$s and $4$s - try to count how many don't use each floor at least once, and subtract.
Hint for the second: there are $\binom 52$ ways to choose the two people who want floor $3$. For each choice, we then have to assign $2$ or $4$ to each of the other three, but we can't assign the same floor to all three of them.