Question

Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. Firstly the women chooses the chair from the set numbered $\{1,2,3,4\}$ then men selected the remaining chairs. The number of possible arrangements are

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

Answer 1

Answer: (C)

${}^4{P}_2{\times }^6{P}_3$

SInce the women choose first that also from the set of $\{1,2,3,4\}$
Hence the number of ways the seats of two women could be filled is
${}^4{P}_2$
Now out of the total 8 seats 2 are taken, hence 6 remain , and in total there are 3 men.
Hence the permutation to fill the men's seats will be
${}^6{P}_3$
Hence the required permutation will be
${}^4{P}_2.{}^6{P}_3$