Question

A delegation of four friends to be selected from a group of $12$ friends. The number of ways the delegation be selected if two particular friends refused to be together and two other particular friends wish to be together only in the delegation.

• A. 226
• B. 114
• C. 156
• D. 170

Answer 1

Answer: (A)

226

Let $A,B$ wish to sit together and $C,D$ do not wish to sit together.
Then following cases arise.
(1) $A,B,C$ are selected and $D$ is not selected ${=}^8{C}_1$
(2) $A,B,D$ are selected and $C$ is not selected ${=}^8{C}_1$

(3) $A,B$ are selected and $C,D$ are not selected ${=}^8{C}_2$
(4) $D$ is selected and $A,B,C$ are not selected ${=}^8{C}_3$

(5) $C$ is selected and $A,B,D$ are not selected ${=}^8{C}_3$

(6) None of these are sleected ${=}^8{C}_4$

$\therefore$ Number of ways $=226$