Question

In an examination paper there are two groups, each containing 4 questions. A candidate is required to attempt 5 questions but not more than 3 questions from any group. In how many ways can 5 questions be selected?

• A. 24
• B. 48
• C. 96
• D. None of these

Answer 1

The Correct Option is B

The correct option is (B): 48
The problem requires selecting 5 questions from two groups of 4 questions each, with the restriction that not more than 3 questions can be selected from any group.

Step 1: Understand the possibilities
To satisfy the condition that no more than 3 questions can be selected from any group, the possible combinations of questions from Group 1 and Group 2 are:

- 3 questions from Group 1 and 2 questions from Group 2
- 2 questions from Group 1 and 3 questions from Group 2

Step 2: Calculate each case
1. Selecting 3 questions from Group 1 and 2 questions from Group 2:
The number of ways to choose 3 questions from 4 in Group 1 is \(C\binom{4}{3}\), and the number of ways to choose 2 questions from 4 in Group 2 is \(C\binom{4}{2}\).

  So, the number of ways is:
  \(C\binom{4}{3}\) \times \(C\binom{4}{2}\) = 4 \times 6 = 24\]

2. Selecting 2 questions from Group 1 and 3 questions from Group 2:
  The number of ways to choose 2 questions from 4 in Group 1 is \( \binom{4}{2} \), and the number of ways to choose 3 questions from 4 in Group 2 is \( \binom{4}{3} \).

  So, the number of ways is:
  \[\binom{4}{2} \times \binom{4}{3} = 6 \times 4 = 24\]

 Step 3: Total number of ways
The total number of ways to select the questions is:
\[24 + 24 = 48\]

Final Answer:
The number of ways to select 5 questions is 48.