6. 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.
- Show that the probability that the first two contestants to be eliminated are both male is \(\frac { 2 } { 15 }\).
- Find the probability that more females than males are eliminated in the first three rounds of the game.
- Given that the first contestant to be eliminated is male, find the probability that the next two contestants to be eliminated are both female.
(3 marks)