For any floor, the chance on x number of people going there can be modelled with a binomial distribution of Bin(10, 1/10) (the same as throwing a ten-sided dice once for every person).

So the chance of a floor having 0 people is

The chance of x number of floors having 0 people is again a binomial Bin(10, 0.35) of which the expected value is 10 * 0.35 = 3.5

For (b) I assume you mean there are 5 people in the elevator.

This changes the initial binomial to Bin(5, 1/10) for which

The chance of x number of floors with 0 people becomes Bin(10, 0.59). The expected value of that is 10 * 0.59 = 5.9