Question

$\text{Column - 1 and 2 consist of different words, number of selection of 3 letters from the word respectively.}$

$\begin{array}{cccc}& \text{Column-I}& & \text{Column-II}\\ \left(I\right)& DREAM& \left(P\right)& 70\\ \left(II\right)& DEDICATION& \left(Q\right)& 10\\ \left(III\right)& POWERFUL& \left(R\right)& 77\\ \left(IV\right)& COMBINATION& \left(S\right)& 56\end{array}$

$\text{Which of the following is the only CORRECT combination?}$

• A. $\left(I\right)\to \left(P\right)$
• B. $\left(II\right)\to \left(Q\right)$
• C. $\left(III\right)\to \left(S\right)$
• D. $\left(IV\right)\to \left(Q\right)$

Answer 1

The correct option is C $\left(III\right)\to \left(S\right)$

$\text{Number of ways 3 letters can be selected from the}\text{given words is as follows:}$
$\underset{–}{\text{DREAM}}\text{3 letters can be selected out of 5 different letters}\text{in number of ways}{=}^5{C}_3=10$
$\underset{–}{\text{DEDICATION}}\text{There can be two cases possible.}{\text{All distinct letters can be selected in}}^8{C}_3\text{ways.}{\text{1 pair and 1 distinct can be selected in}}^2{C}_1{\times }^7{C}_1\text{ways}\therefore \text{Total number of ways}{=}^2{C}_1{\times }^7{C}_1{+}^8{C}_3=70$
$\underset{–}{\text{POWERFUL}}\text{3 letters can be selected out of 8 different letters}\text{in number of ways}{=}^8{C}_3=56$
$\underset{–}{\text{COMBINATION}}\text{There can be two cases possible.}{\text{All distinct letters can be selected in}}^8{C}_3\text{ways.}{\text{1 pair and 1 distinct can be selected in}}^3{C}_1{\times }^7{C}_1\text{ways}\therefore \text{Total number of ways}{=}^3{C}_1{\times }^7{C}_1{+}^8{C}_3=77$