Suppose a small cinema with one screen has 5 screenings per day.

5. Suppose a small cinema with one screen has 5 screenings per day. The film distributor has offered them 7 different films that they might screen (we will assume that none are particularly long, so the choice of films to show does not affect the available number of screenings). Given that we are only interested in which films they are going to screen, not the order in which they show them, how many possible choices are there

(a) If they choose to show all different films?

(b) If three of the films are classified as "blockbusters" and they want to choose at least two blockbusters to be shown?

(c) If they allow the possibility of showing the same film multiple times, and still want at least two screenings to be blockbusters (not necessarily different)?

(d) If films can be repeated, they need at least two blockbuster screenings, but no film is to be shown more than 3 times throughout the day?