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.