Excessively Demanding SchoolDiscrete Mathematics Level 4
At Peter's school, to progress to the next year he has to pass an exam every summer. Every exam is out of 50 and the pass mark is always 25. As there are 11 year groups, to leave the school he must pass 10 exams. Since Peter's work ethic increases with age, his scores never decrease.
Let \(N\) be the number of different series of marks Peter could have achieved, given that he left school without ever failing an exam. What are the last 3 digits of \(N\)?
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