Question

What is the minimum number 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 same state?

Answer 1

Answer:

4951 students

Step-by-step explanation:

If there was 99 students from each state, that would make the total to be:

99 * 50 = 4950

We can use the pigeon hole principle to make this the minimum number required.

The pigeon hole principle basically tells us that if you have more "pigeons" than "holes" then there must be one hole with multiple objects in it.

So, using this idea, we see that:

we need at least 1 more to ensure this

So, min number required would be

4950 + 1 = 4951