$2$ boys and $2$ girls are in Room $X$,and $1$ boy and $3$ girls are in Room $Y$. Specify the sample space for the experiment in which a room is selected and then a person.

(N/A) Let us denote the $2$ boys and $2$ girls in Room $X$ as $B_{1}, B_{2}$ and $G_{1}, G_{2}$ respectively.
Let us denote the $1$ boy and $3$ girls in Room $Y$ as $B_{3}$ and $G_{3}, G_{4}, G_{5}$ respectively.
When a room is selected first and then a person,the possible outcomes are the combinations of the room and the individuals within that room.
Thus,the required sample space $S$ is given by:
$S = \{X B_{1}, X B_{2}, X G_{1}, X G_{2}, Y B_{3}, Y G_{3}, Y G_{4}, Y G_{5}\}$