# CBSE Class 9 Answered

**Professor Trig prepared a question paper which contains 8 problems to test his post graduate students. Each student was given 3 of them. No two students received more than one common problem. What is the largest possible number of students?**

Asked by ketkiparasgandhi | 24 Jun, 2023, 01:56: PM

Expert Answer

There are 2 different cases:

Case 1: When all 3 questions are different

Only 2 set of 3 questions can be made.

Case 2: When only one question is common

Keeping Q1 common, there are

^{7}C_{2}ways to pick 2 different questionsSimilarly, keeping Q2 common, again there are there are

^{7}C_{2}ways to pick 2 different questionsSame applies to Q3, Q4, Q5, Q6, Q7, Q8

There are 8 x

^{7}C_{2}waysSo, the largest number of students = 2 + 8 x

^{7}C_{2}= 2 + (8 x 7 x 3) = 2 + 231 = 233
Answered by Renu Varma | 26 Jun, 2023, 11:18: AM

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