find the minimum number of students needed to guarantee that 5 of them belong to same class ( freshman, sophomore, junior, senior)
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Answer:
The minimum number of students needed to guarantee that 5 of them belong to the same class is 17.
Explanation:
To solve this problem, we can use the pigeonhole principle. We have 4 classes and we want to find the minimum number of students needed to guarantee that 5 of them belong to the same class.
Assume that we have n students.
The worst-case scenario is when we have n-1 students distributed evenly among the 4 classes (i.e., each class has floor((n-1)/4) students). In this case, the largest possible number of students in each class is floor((n-1)/4) + 1.
Therefore, if we add one more student, we will have at least one class with at least 5 students (since floor((n-1)/4) + 1 >= 5 when n >= 17).
Hence, the minimum number of students needed to guarantee that 5 of them belong to the same class is 17.
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