pigeonhole principle clarification 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?

You can have $99$ students from each state before you get $100$ students from at least one state.  
So construct a pigeon hole for each state. Then add the maximum number under the desired number to each one.  So we get $99 \times 50 = 4950$ students. Then, the next one we add will push any single pigeon hole to $100$ pigeons students.  So the minimum number of students for there to be 100 from at least one state is $(99 \times 50) + 1 = 4951$
