Multiple choice

There are 20 questions in a question paper. If no two students solve the same combination of questions but solve equal number of questions then the maximum number of students who appeared in the examination is

  1. $\displaystyle ^{20}C_9$
  2. $\displaystyle ^{20}C_{11}$
  3. $\displaystyle ^{20}C_{10}$

  4. none of these
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C Correct answer
Explanation

To have the maximum number of students solving an equal number of questions with unique combinations, we look for the maximum value of nCr, which occurs at the middle term. For n=20, this is 20C10.

AI explanation

The maximum number of students occurs when the number of combinations of questions solved is at its peak, which happens when each student solves exactly half of the 20 questions. Therefore, we must find the maximum binomial coefficient for n = 20, which is 20C10. This represents the number of ways to choose 10 questions out of 20, giving a maximum of 20C10 students.

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