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?

Me and my friend are stuck on this question he thinks the answer to part a) is 1.

and the answer to part b is 0.5. But for part b) i think the answer has to be more the 5 anyway so i think he is wrong.

I would apprecate any help as i dont even know which distribution to use.