[High School Probability] Giveaway Contest Odds - personal puzzle I want to solve properly

If I understand you correctly, there will be 510 people in the contest once your friends have entered, and you want to know the likelihood that at least one of the 11 of you wins a book?

Think about it this way. There are 510 numbers in a hat, and 50 are drawn consecutively. What is the probability that none of the numbers 1, ..., 11 are drawn? For the first draw, this is 499/510. For the second, there is now one less number in the hat, but all of the numbers 1, ..., 11are still there. So the probability is 498/509. For the third draw, it is 497/508, and so on.

In all the probability that none of you  gets a book is

(499.498...451.450)/(510.509....462.461) = approx. 0.3176.

So the likelihood that at least one of you wins a book is about 68.24%.
If someone wins book #1, can they win another book or are they out of the drawing?
I think that math really boils down to what numbers you're given. If you're given some numbers you will get this answer, but another set gets a totally different one! So when you are given the numbers that you are given, just make sure you know what they are because if they're A then you will get B but if they're C then you will get something different like D or E.

Do you get it now?