To solve this problem, we can use the Pigeonhole Principle. The Pigeonhole Principle states that if you want to distribute n items into m containers and n m, then at least one container must contain more than one item.

1. In this case, the 'items' are the students and the 'containers' are the states. We want to find the minimum number of students needed to guarantee that at least one state (container) has at least 100 students (items).

2. Since there are 50 states, if each state had 99 students, that would total 4950 students (99 students/state * 50 states = 4950 students).

3. However, this would mean that no state has 100 students. So, to guarantee that at least one state has 100 students, we would need to add one more student to our total.

4. Therefore, the minimum number of students needed to guarantee that at least one state has 100 students is 4950 students + 1 student = 4951 students.

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To solve this problem, we can use the Pigeonhole Principle. The Pigeonhole Principle states that if you want to distribute n items into m containers and n > m, then at least one container must contain more than one item.

1. In this case, the 'items' are the students and the 'containers' are the states. We want to find the minimum number of students needed to guarantee that at least one state (container) has at least 100 students (items).

2. Since there are 50 states, if each state had 99 students, that would total 4950 students (99 students/state * 50 states = 4950 students).

3. However, this would mean that no state has 100 students. So, to guarantee that at least one state has 100 students, we would need to add one more student to our total.

4. Therefore, the minimum number of students needed to guarantee that at least one state has 100 students is 4950 students + 1 student = 4951 students.

Knowee AI · Accepted Answer

To solve this problem, we can use the Pigeonhole Principle. The Pigeonhole Principle states that if you want to distribute n items into m containers and n > m, then at least one container must contain more than one item.

1. In this case, the 'items' are the students and the 'containers' are the states. We want to find the minimum number of students needed to guarantee that at least one state (container) has at least 100 students (items).

2. Since there are 50 states, if each state had 99 students, that would total 4950 students (99 students/state * 50 states = 4950 students).

3. However, this would mean that no state has 100 students. So, to guarantee that at least one state has 100 students, we would need to add one more student to our total.

4. Therefore, the minimum number of students needed to guarantee that at least one state has 100 students is 4950 students + 1 student = 4951 students.

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

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