The elevator in the Math and Computer Building can stop at one of six ?oors. Four riders get on the elevator at the ?rst ?oor and the elevator heads up. Each rider picks a ?oor at random (from ?oor 2 to ?oor 6) and gets off, and it is possible for more than one passenger to get off at any ?oor.

a) Describe, in words (no need to list all possibilities), S, the sample space for this experiment. Be sure to include the total number of points in S.

b) Assuming the points in S to be equally probable, ?nd: i) the probability that nobody gets off at the second ?oor.

ii) the probability that nobody gets off at the odd numbered ?oors

iii) the probability that half of the riders get off at the same ?oor and the other half get off at a different ?oor.

c) Generalize the results in i), ii) and iii) for r riders and n ?oors. Assume both r and n are even.