Question

Eight chairs are numbered $1$ to $8$. Two women and three men wish to occupy one chair each. First, the women choose the chairs from amongst the chairs marked $1$ to $4$, and then the men select the chairs from amongst the remaining. The number of possible arrangements is

• A. ${}^6{C}_3{\times }^4{C}_2$
• B. ${}^4{P}_2{\times }^4{P}_3$
• C. ${}^4{C}_2{+}^4{P}_3$
• D. None of these

Answer 1

Answer: (D)

None of these

$\overline{1}\overline{2}\overline{3}\overline{4}\overline{5}\overline{6}\overline{7}\overline{8}$
Two women can chose two chairs out of $1,2,3,4$ in ${}^4{C}_2$ ways, and can arrange among themselves in $2!$ ways. Three men can choose $3$ chairs out of $6$ remaining chairs in ${}^6{C}_3$ ways and can arrange themselves in $3!$ ways.
Therefore, total number of possible arrangements is ${}^4{C}_2\times 2!{\times }^6{C}_3\times 3!{=}^4{P}_2{\times }^6{P}_3$.