Verified Solution • 2025–26 Session moderate

QJEEM24Mae72e: JEE Main 2024 Mathematics - Class 11 JEEM24Mae72e Solution: In an examination of Mathematics paper, there are 20 questions…

In an examination of Mathematics paper, there are 20 questions of equal marks and the question paper is divided into three sections : A,BA, B and CC . A student is required to attempt total 15 questions taking at least 4 questions from each section. If section AA has 8 questions, section BB has 6 questions and section CC has 6 questions, then the total number of ways a student can select 15 questions is __________.

Step-by-Step Verified Solution

The problem involves choosing 15 questions out of a total of 20 available questions, with the constraint that at least 4 questions must be chosen from each of the three sections A, B, and C. To evaluate the total number of ways a student can select these questions, we need to consider every possible combination of questions from sections A, B, and C that sum up to 15 questions while respecting the constraints.

Section A has 8 questions, Section B and C each have 6 questions. The student must choose at least 4 questions from each section, which satisfies the minimum requirement. However, since the student is to attempt a total of 15 questions, there are several combinations to consider, as outlined below:

  • Choosing 4 questions from A, 5 from B, and 6 from C
  • Choosing 4 questions from A, 6 from B, and 5 from C
  • Choosing 7 questions from A, 4 from B, and 4 from C
  • Choosing 6 questions from A, 5 from B, and 4 from C
  • Choosing 6 questions from A, 4 from B, and 5 from C
  • Choosing 5 questions from A, 5 from B, and 5 from C
  • Choosing 5 questions from A, 6 from B, and 4 from C
  • Choosing 5 questions from A, 4 from B, and 6 from C

Aamp;Bamp;Camp;⇒amp; No. of  question 4amp;5amp;6amp;→amp;8C46C56C64amp;6amp;5amp;→amp;8C46C66C57amp;4amp;4amp;→amp;8C76C46C46amp;5amp;4amp;→amp;8C66C56C46amp;4amp;5amp;→amp;8C66C46C55amp;5amp;5amp;→amp;8C56C56C55amp;6amp;4amp;→amp;8C56C66C45amp;4amp;6amp;→amp;8C56C46C6\begin{array}{|c|c|c|l|c|}\hline \mathrm{A} & \mathrm{B} & \mathrm{C} & \Rightarrow & \begin{array}{c}\text { No. of } \\\text { question }\end{array} \\\hline 4 & 5 & 6 & \rightarrow & { }^8 C_4{ }^6 C_5{ }^6 C_6 \\\hline 4 & 6 & 5 & \rightarrow & { }^8 C_4{ }^6 C_6{ }^6 C_5 \\\hline 7 & 4 & 4 & \rightarrow & { }^8 C_7{ }^6 C_4{ }^6 C_4 \\\hline 6 & 5 & 4 & \rightarrow & { }^8 C_6{ }^6 C_5{ }^6 C_4 \\\hline 6 & 4 & 5 & \rightarrow & { }^8 C_6{ }^6 C_4{ }^6 C_5 \\\hline 5 & 5 & 5 & \rightarrow & { }^8 C_5{ }^6 C_5{ }^6 C_5 \\\hline 5 & 6 & 4 & \rightarrow & { }^8 C_5{ }^6 C_6{ }^6 C_4 \\\hline 5 & 4 & 6 & \rightarrow & { }^8 C_5{ }^6 C_4{ }^6 C_6 \\\hline\end{array}

Total ways of select =11376=11376

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