Answer to Question #142101 in Discrete Mathematics for Promise Omiponle

Question #142101

Assume that a class consists only of students residing the 50 US states. Find the smallest number of students that must be enrolled in a class to guarantee that there are at least 5 students from the same state

Expert's answer

If a class contains 4 students from each state, then there are 4•50=200 all such students. Then by Pigeonhole principle, to guarantee that there are at least 5 students from the same state the smallest number of students that must be enrolled in a class is 200+1=201.

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Shubhang Mehrotra

06.11.20, 16:47

Using PigionHole Principle, with the number of students as 'x', and number of states as 'holes' = 50. CEIL(x/50) = 5 Since, CEIL(200/50) = 4. CEIL(201/50) = 5. Therefore, the Minimum number of students = 201.

Answer to Question #142101 in Discrete Mathematics for Promise Omiponle

If a class contains 4 students from each state, then there are 4•50=200 all such students. Then by Pigeonhole principle, to guarantee that there are at least 5 students from the same state the smallest number of students that must be enrolled in a class is 200+1=201.

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