Multiple choice

In an examination, the question paper consists of $10$ questions which are equally divided into two sections $a$ and $b$. A student has to attempt a total of six questions by attempting at least two from each section. In how many ways can the student select the questions?

  1. $200$
  2. $180$
  3. $300$
  4. $360$
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A Correct answer
Explanation

Section A has 5 questions, Section B has 5. Need 6 questions total, at least 2 from each. Cases: (2A, 4B) = 5C2 * 5C4 = 10 * 5 = 50. (3A, 3B) = 5C3 * 5C3 = 10 * 10 = 100. (4A, 2B) = 5C4 * 5C2 = 5 * 10 = 50. Total = 50 + 100 + 50 = 200.

AI explanation

The 10 questions are divided into two sections of 5 questions each, and the student must attempt 6 questions with at least 2 from each section. Using the method of combinations, the valid distribution of 6 questions between the two sections can be 2 from the first and 4 from the second, or 3 from the first and 3 from the second, or 4 from the first and 2 from the second. We calculate the ways for each case as 5C2 x 5C4, 5C3 x 5C3, and 5C4 x 5C2. Adding these gives 10 x 5 + 10 x 10 + 5 x 10 = 50 + 100 + 50 = 200. The total number of ways to select the questions is 200.

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