9 friends are trying to allocate 27 football teams between them (3 each in total), they want to make the distribution process as fair as possible. Assuming that 1 out of the 27 teams is seen as desirable and the other 26 out of 27 are seen as equal, is there a difference if either:
A) The 1st person draws 3 teams, then the 2nd person draws 3 teams, then the 3rd... etc. Or,
B) Each person draws 1 team consecutively until there are none left?
We were also wondering if there is a higher probability of anyone getting the desirable team, depending on if they go 1st, 2nd, etc... or not?
My attempt to answer this question was as follows:
for process A, I calculated the probability that the 1st person would not get the desirable team: $$\frac{26}{27}\cdot\frac{25}{26}\cdot\frac{24}{25}=\frac{8}{9}$$ and then the probability that the 2nd person would not get the desirable team = Probability that the 1st person would get the desirable team or probability that 1st person would not get the desirable team and probability that the 2nd person would not get the desirable team: $$\frac{1}{9} + \frac{8}{9}\cdot (\frac{23}{24}\cdot\frac{22}{23}\cdot\frac{21}{22})=\frac{8}{9}.$$
Since these probabilities coincide it seemed like going first was not an advantage in process A, however, I am not sure if this makes sense.