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. $^6C_3 \, \times \, ^4C_2$
• B. $^4P_2 \, \times \, ^4P_3$
• C. $^4C_2 \, \times \, ^4P_3$
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

Since, the first 2 women select the chairs amongst 1 to 4 in $^4P_2$ ways. Now, from the remaining 6 chairs, three men could be arranged in $^6P_3$
$\therefore$ Total number of arrangements = $^4P_2 \, \times \, ^6P_3$