Although this is based on a book/film I think the question itself is more GQ.

Just watched Hunger Games: Catching fire and wondering at the mathematics of the reaping. Minor spoilers for the film follow.

So, there have been 74 Hunger Games, and in that period there is at least 1 male and 1 female from all 12 districts, all 24 possible winners have happened once. That seems unlikely to me even if everybody had an equal chance, but they stated that the richer districts won much more often.

So could somebody do the maths for me?

i)In 74 attempts with 24 possibilities, what is the chance that every possibility happens at least once, assuming each possibility is equally likely?

ii)Judging by the ages of the characters, none of them seemed to have won more than 40 years ago, (except Mags, but she was volunteering for a much younger woman so the younger one could have been there instead). What are the odds of all 24 possibilities coming up in a **40** year period?