I have a

pool of participants - defined

number of tournaments (competitions) - defined

participants per tournament (partPerTour)

Of the participants per tournament only 1 winner (the one with highest ranking) is put forward, everyone else is returned back to the pool for the next tournament.

I have calculated the probability of a specific participant (the one with highest ranking in the whole pool) being picked.

For this I use programming (I need to code it in the end) and just loop through the following

repeat for number of tournaments and add up

tour1:[1/(pool)]+[1/(pool-1)]...+[1/(pool-participantsPerTournament)]+

....+...+

tourx:[1/(pool-x+1)]+[1/(pool-x+1-1)]...+[1/(pool-x+1-participantsPerTournament)]

(pool is reduced by 1 participant from tournament to tournament)

But I would like to also calculate how many participants I need per tournament to have a given probability of picking a specific participant met.

I assume this is probably quite a standard probability calculation, and there might be a formula, but I can't find the right one.

Any insight are appreciated!