UPPCL AE 2018:66

Question

In a course, a professor gives five grades $\{\text{A, B, C, D, F}\}.$ What is the minimum number of students required so that four of them are guaranteed to get the same grade?

• A. None of the above
• B. $14$
• C. $18$
• D. $16$ 

Answer 1

Worst case:

Grade          No. of Students

  A:                            3

  B:                            3

  C:                            3

  D:                            3

  F:                             3

still none of the grade have been given to 4 Students. Lets increase one more Student Whatever be his/her grade(A/B/C/D/F),One of the grade must have given to  4 students.So (3+3+3+3+3) + 1 = 16. Minimum 16 students are required.