The question and the answer are both a bit clumsy here.
They are saying, than the T-shirt can be found in eighth attempt. No one knows if they wanna say,
- The selection process puts the shirts into a random order, and we have a "success" if the shirt is in any of the first eight positions (first interpretation).
- Or under the assumption that "success" means finding the medium shirt only on the eighth attempt, not earlier.
The word CAN here doesn't signifies surety.
The proposed solution on the website makes the absurd claim that the probability not to find a medium shirt on the first attempt is 8/13. That would be the correct probability if the problem statement said there were five medium shirts, but the problem statement clearly says there is only one. Hence the correct probability is 12/13. The remaining probabilities are as 11/12 * 10/11* 9/10....and so on.
(Under the assumption that "success" means finding the medium shirt only on the eighth attempt, not earlier) the probability to be in the eighth position is 1/13
Now, by directly computing P(L′1∩L′2∩L′3∩L′4∩L′5∩L′6∩L′7∩L8) as proposed in the solution on the website, it is attributable to the fact that we computed the probabilities correctly and they gave the wrong probabilities. You need only make the obvious cancellations in order to obtain a simple fraction as the solution.
Still we can't give a correct solution to an incorrect question. So I guess, everyone's assumption would be right here. And marks should be given to all.
