Multiple choice

In an examination, a student has to answer $4$ questions out of $5$ questions; Questions $1$ and $2$ are however compulsory. The number of ways in which the student can make a choice is :

  1. $6$
  2. $3$
  3. $2$
  4. $60$
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B Correct answer
Explanation

The student must choose 4 questions out of 5. Questions 1 and 2 are compulsory, so the student must choose 2 more questions from the remaining 3 (5 - 2 = 3). The number of ways is 3C2 = 3.

AI explanation

The student must answer compulsory questions 1 and 2, so 2 questions out of the required 4 are already chosen. This leaves 3 optional questions (questions 3, 4, and 5) from which the student must choose the remaining 2 questions. Using the combination formula nCr, the number of ways to choose 2 questions from 3 is 3C2. Calculating 3C2 gives 3 divided by 1 times 2, resulting in 3 ways.

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