There are three sections in a question paper, each containing 4 questions. If a candidate has to answer only…

There are three sections in a question paper, each containing 4 questions. If a candidate has to answer only 5 questions from this paper without leaving any section, then number of ways the candidate can make the choice of questions is
  1. 624
  2. 704
  3. 384
  4. 432

Solution

Number of ways to select 5 questions from these sections as follows, $ A \quad B \quad C $ Section $\{\begin{array}{lll}2 & 2 & 1 \\ 2 & 1 & 2 \\ 1 & 2 & 2\end{array}$ $\begin{gathered} \left\{\begin{array}{lll} 3 & 1 & 1 \\ 1 & 3 & 1 \\ 1 & 1 & 3 \end{array}\right. \\ \Rightarrow{ }^4 C_2 \times{ }^4 C_2 \times{ }^4 C_1 \times 3+{ }^4 C_3 \times{ }^4 C_1 \times{ }^4 C_1 \times 3 \\ \Rightarrow \frac{4 !}{2 ! 2 !} \times \frac{4 !}{2 ! 2 !} \times \frac{4 !}{1 ! 3 !} \times 3+\frac{4 !}{3 ! 1 !} \times \frac{4 !}{1 ! 3 !} \times \frac{4 !}{1 ! 3 !} \times 3 \\ \Rightarrow 432+192=624 \end{gathered}$

Asked in: AP EAMCET 2018 (24 Apr Shift 1)

Practice more Permutation Combination questions on Aicharya