An elevator in a ten-floor building leaves the first floor with six passengers. Assuming all possible outcomes to be equally likely, find the probabilities of the following events.

(a) Three passengers will get off the elevator on the second floor, one passenger on the third floor, and two on the fifth.

(b) Three passengers will get off on the second floor, and one on the third.

(c) No two passengers will get off on the same floor.

(d) Two passengers will get off on the same floor, and four more on another floor.

(e) Two passengers will get off on the same floor, and three more on another floor.