Excessively Demanding School
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. To graduate from 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 \(N\)?