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2{\text{ boys and 2 girls are in room }}X{\text{ and 1 boy and 3 girls are in room }}Y{\text{ specify the sample space for the }} \\

{\text{experiment in which a room is selected and then a person}}{\text{. }} \\

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{\text{let us denote 2 boys and 2 girls in a room X as }}{{\text{b}}_1},{b_2}{\text{ and }}{{\text{g}}_1},{g_2}{\text{respectively}}{\text{.}} \\

{\text{let us denote 1 boy and 3 girls in a room Yas }}{{\text{b}}_3}{\text{ and }}{{\text{g}}_3},{g_4},{g_5}{\text{ respectively}}{\text{.}} \\

{\text{now the sample space which we get in that room is choosen first }} \\

{\text{suppose we choose room X then we will choose boys and girls of room X only }} \\

{\text{and if we choose room Y we will choose boys and girls of room Y only}} \\

{\text{so the sample space will be }}\left\{ {{\text{X}}{{\text{b}}_1},{\text{X}}{{\text{b}}_2},{\text{X}}{{\text{g}}_1},{\text{X}}{{\text{g}}_2},{\text{Y}}{{\text{b}}_3},{\text{Y}}{{\text{g}}_3},{\text{Y}}{{\text{g}}_4},{\text{Y}}{{\text{g}}_5}} \right\} \\

{\text{NOTE:in these type of questions if we choose room X then we will choose boys and girls of room X only }} \\

{\text{ and if we choose room Y then we choose boys and girls of room Y only}}{\text{.}} \\

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{\text{let us denote 2 boys and 2 girls in a room X as }}{{\text{b}}_1},{b_2}{\text{ and }}{{\text{g}}_1},{g_2}{\text{respectively}}{\text{.}} \\

{\text{let us denote 1 boy and 3 girls in a room Yas }}{{\text{b}}_3}{\text{ and }}{{\text{g}}_3},{g_4},{g_5}{\text{ respectively}}{\text{.}} \\

{\text{now the sample space which we get in that room is choosen first }} \\

{\text{suppose we choose room X then we will choose boys and girls of room X only }} \\

{\text{and if we choose room Y we will choose boys and girls of room Y only}} \\

{\text{so the sample space will be }}\left\{ {{\text{X}}{{\text{b}}_1},{\text{X}}{{\text{b}}_2},{\text{X}}{{\text{g}}_1},{\text{X}}{{\text{g}}_2},{\text{Y}}{{\text{b}}_3},{\text{Y}}{{\text{g}}_3},{\text{Y}}{{\text{g}}_4},{\text{Y}}{{\text{g}}_5}} \right\} \\

{\text{NOTE:in these type of questions if we choose room X then we will choose boys and girls of room X only }} \\

{\text{ and if we choose room Y then we choose boys and girls of room Y only}}{\text{.}} \\

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