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?

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?

Solution:
5 questions can be selected in the following ways,
2 question from first group and 3 question from second group Or 3 question from first group and 2 question from second group.
= (⁴C₂ × ⁴C₃) + (⁴C₃ × ⁴C₂)
= 24 + 24
= 48