What is the minimum numbers of students each of whom comes f

What is the minimum numbers of students, each of whom comes from one of the 50 states, who must be enrolled in a university to guarantee, that there are at least 100 who come from the state?

Solution

If there were 99 students from every 50 states

After that there would be 4950 students registered without having 100 from the same state.

If one additional student registered, afterward that student would be the 100th student from one of the states.

So, the minimum number is 4951.

i.e, 50*99+1 = 4951