There is a raffle a state holds annually to assign salmon fishing licenses to fisherman; in a specific stetch of river, to control harvest and limit access, to ensure resource management and a high quality recreational experience.
There are 772 licenses available up for grabs in the draw. There are 1,256 applicants in the draw. The draw is random and sequential. However, there is a catch: applicants can apply as a 'party' of up 5 members. If a 'party' is drawn and sufficient licenses remain at that trial of the drawing, all members of the party get licenses. Then, the amount of licenses available for the next round of the drawing is reduced by the number awarded; and so on, until all 772 licenses are awarded. If on the last trial less licenses remain than the number in the party, the state simply awards tags to all in that party and the draw is over. There is no way of knowing a priori how many of the 1,272 applicants are individual applicants or parties consisting of 2, 3, 4 or 5 members.
How would the odds of drawing a license be calculated for this problem? Many thanks, in advance!