Hey all. I would really appreciate it if someone could help me out with this question. Thanks!

In a sales campaign, a petrol company gives each motorist who buys their petrol a card with a picture of a film star on it. There are 10 different pictures, one each of 10 different film stars, and any motorist who collects a complete set of all 10 pictures gets a free gift. On any occasion when a motorist buys petrol, the card received is equally likely to carry any one of the 10 pictures in the set. Two of the ten film stars in the set are X and Y.

Find the probability that the first four cards received results in the motorist having

(i) all different pictures

(ii) exactly three different pictures

(iii) a picture of X or of Y or of both.

At a certain stage, the motorist has collected nine of the ten pictures. Find the least value of n such that P(at most n more cards are needed to complete the set) > 0.99