Would the following statement be applicable to the pigeonhole principle? Or can I simply do $100 \times 50 = 5000$?
What is least amount of students in a school to guarantee that there are
at least 100 students from the same state?
[Math] pigeonhole principle clarification
combinatoricspigeonhole-principleprobability
Best Answer
Your answer is not quite correct. The most you can have WITHOUT having 100 students from the same state is $50\cdot99=4950$; so, the minimum to guarantee it is $4950+1=4951$.
Although I didn't say 'by the Pigeonhole principle', that's what has happened here.