In an examination of Mathematics paper, there are 20 questions of equal marks and the question paper is divided into three sections : A,B and C. A student is required to attempt total 15 questions taking at least 4 questions from e...
Answer: 11376
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Official 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 CChoosing 4 questions from A, 6 from B, and 5 from CChoosing 7 questions from A, 4 from B, and 4 from CChoosing 6 questions from A, 5 from B, and 4 from CChoosing 6 questions from A, 4 from B, and 5 from CChoosing 5 questions from A, 5 from B, and 5 from CChoosing 5 questions from A, 6 from B, and 4 from CChoosing 5 questions from A, 4 from B, and 6 from C
ABC⇒456→8C46C56C6465→8C46C66C5744→8C76C46C4654→8C66C56C4645→8C66C46C5555→8C56C56C5564→8C56C66C4546→8C56C46C6
Total ways of select =11376