# Probabilities of Drawing

Assume there is a group of people trying to draw a "ticket" out of many different types of "tickets".

Each individual applicant must indicate their top 3 types of "tickets" in order of priority as part of their application: 1st choice, 2nd choice, 3rd choice.

Once I know the Individual A's three choices, I know how many of those types of "tickets" are available in their 1st choice, their 2nd choice and their 3rd choice.

I also know how many other individuals have selected that type of "ticket" as one of the 1st, 2nd or 3rd choice.

Each individual is randomly chosen and then their 3 choices are considered. If their 1st choice still has available "tickets" then they receive that ticket. However if their are no more tickets available for their first choice, then their 2nd choice will be considered and so on until their 3rd choice.

How do you calculate the probability of drawing a ticket? Do you do the probability at your 1st choice level and then 2nd choice level and then 3rd choice level and combine those probabilities? If so, how do you combine those probabilities? Does the order of your choices matter? Any insight helps.