Question

Number of ways in which $3$ boys and $3$ girls can be seated on a line where two particular girls do not want to sit adjacent to a particular boy is equal to

• A. $36$
• B. $72$
• C. $144$
• D. $288$

Answer 1

The correct option is D $288$

Let $B_1$ be the boy & $G_1,G_2$ be the girls who donot want to sit with $B_1$
$\times \times \times \times \times \times$
1 2 3 4 5 6
If $B_1$ occupies first place then $G_1$ or $G_2$ cannot sit on second place
$\Rightarrow$ Number of ways${=}^4{P}_2\times 3=72$ ways
If $B_1$ occupies 6th placesimilarly number of ways = 72 ways
Now if $B_1$ sit at 2nd place,number of ways ${=}^3{P}_2\times 3=36$ ways
Similarly $B_1$ can sit on 3rd, 4th, 5th place in same number of ways = 36
$\Rightarrow$ Total ways $=72\times 2+36\times 4=288$ ways