An elevator goes from the ground floor up to the 8th floor (8 floors in total). In the elevator 10 people. Each one of them choose randomly and independently with the other people in which floor to get off the elevator. The expected value (mean) of the number floors in which no one came off at is:

a. 6 b. 8 c. 8*(7/8)^10 d. 10*(1/8)^10 e. 10*(7/8)^8

the correct answer should be "e". why ?

cheers