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UGC NET Computer Science Dec 2022 Shift I (Paper II)

What is the minimum number of students in a discrete mathematics class to be sure that at least six will receive the same grade, if there are seven possible grades: S, A, B, C, D, P and F?

Solution

There are $7$ possible grades. To avoid getting $6$ students in the same grade, maximum $5$ students can receive each grade. So, maximum students without guarantee: $7\times 5=35$ Now, one more student will surely make at least $6$ students in one grade. Required number of students: $35+1=36$
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