At my work we often run small sweepstakes at big sporting events, e.g. the football world cup, the Olympics, the rugby world cup.
As you may know, the rugby world cup is currently on. There are 20 teams involved, and 11 of us in the office. Using a betting website's odds, we whittled down the 20 teams to the 11 most likely to win outright, and drew them out of a hat.
Of course, each person to draw a team has one fewer potential team than the person who drew previously. The first person to draw has 11 possibilites. The second person has 10. The third has nine, etc.
Of these 11 teams, only three are realistically likely to win. Is it possible to calculate the probability of drawing one of these three at each stage of the draw? If so, is it better to draw earlier or later?