Math Help - help me please

10 people get on the elevator from the ground floor. They are equally likely to get down at any of the 10 floors in the building, and choose their floors independently.

a)Determine the expected number of floors where no one gets down from the elevator.
b)How would your answer change if the 10 people get down in pairs?

i have no idea I think I must have to use a distribution but i am not sure which one i think it was Poisson but this isnt at a fixed interval rate I'm at a loss any clues please aas to what distribution if any that i have to use?????

i thinking instead of using the binomial distribution as it has independent events that do not effect the proabablity of the otehr successses ie getting off the elevator

still confused about the pairs though does anyone have any ideas??