At the start of a gameshow there are 10 contestants of which 6 are female. In each round of

the game, one contestant is eliminated. All of the contestants have the same chance of

progressing to the next round each time.

(a) Show that the probability that the first two contestants to be eliminated are

both male is 2/15

(b) Find the probability that more females than males are eliminated in the first three

rounds of the game.

(c) Given that the first contestant to be eliminated is male, find the probability that the next

two contestants to be eliminated are both female.