There are 5 ping pong balls labelled with numbers 1-5 which will be placed in a lottery machine. During the event, the 5 balls will be drawn and arrive to a combination. The participant that has the combination drawn first wins the top prize, the next unique participant with a matching combination is given the second prize, and so on with the final participant receiving the fourth prize.
Before the lottery, all participants are assigned combinations (out of the 120 possible unique permutations).
I entered a lottery, and have acquired 59 combinations of the 120 unique permutations which can be made from pulling ping pong balls numbered 1 to 5 from a lottery machine. There are only 4 participants, and we have the following amount of the available 120 unique number combinations (no overlap between participants):
Entrant A has 59 combinations, Entrant B has 41 combinations, Entrant C has 13 combinations, Entrant D has 7 combinations,
Once a participant has a combination drawn, they are removed from the lottery and cannot take a further place in the order. I am running into issues determining the odds I end up with a combination which is pulled 3rd or 4th, as Python is not accurately running currently and I am therefore unable to create a Plackett-Luce model code to determine the overall probability per participant per place. Is there a more direct process to obtaining the odds for each participant to end up with ranks 1, 2, 3 & 4?