2 boys and 2 girls are in Room X, and 1 boy and 3 girls in Room Y.

Let us denote 2 boys and 2 girls in room $X$ as $B_{1}, B_{2}$ and $G_{1}, G_{2}$ respectively. Let us denote 1 boy and 3 girls in room $Y$ as $B_{3}$, and $G_{3}, G_{4}, G_{5}$ respectively. Accordingly, the required sample space is given by $S=\left\{X B_{1}, X B_{2}, X G_{1}, X G_{2}, Y B_{3}, Y G_{3}, Y G_{4}, Y G_{5}\right\}$