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

The correct option is D none of these

$\overline{1}\overline{2}\overline{3}\overline{4}\overline{5}\overline{6}\overline{7}\overline{8}$
Two women can choose 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
${}^4{C}_2\times 2!{\times }^6{C}_3\times 3!{=}^4{P}_2{\times }^6{P}_3$.