Que12

Dear Student,
Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{Case}\left(\mathrm{i}\right) \mathrm{When} \mathrm{married} \mathrm{couple} \mathrm{is} \mathrm{choosen} \\ \mathrm{The} \mathrm{we} \mathrm{need} 3 \mathrm{more} \mathrm{people} \mathrm{out} \mathrm{of} 7{=}^7{\mathrm{C}}_3=\frac{7\times 6\times 5}{3\times 2\times 1}=35 \\ \mathrm{Case}\left(\mathrm{ii}\right) \mathrm{When} \mathrm{married} \mathrm{couple} \mathrm{is} \mathrm{not} \mathrm{choosen} \\ \mathrm{The} \mathrm{we} \mathrm{need} 5 \mathrm{people} \mathrm{out} \mathrm{of} 7{=}^7{\mathrm{C}}_5=\frac{7\times 6}{2\times 1}=21 \\ \mathrm{Total} \mathrm{possible} \mathrm{selections}{=}^9{\mathrm{C}}_5 \\ \mathrm{Required} \mathrm{probabilty}=\frac{9\times 8\times 7\times 6}{4\times 3\times 2\times 1}=126 \\ \mathrm{Required} \mathrm{probabilty}=\frac{35+21}{126}=\frac{56}{126}=\frac{4}{9} \left(\mathrm{Answer}\right) \end{gathered}$$

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