Q. 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 men select the chairs from amongst the remaining. The number of possible arrangements is
A) $\ ^{6}C_{3} \times \ ^{4}C_{2}$
B) $\ ^{4}C_{2} \times {\ ^{4}C}_{3}$
C) $\ ^{4}P_{2} \times {\ ^{4}P}_{3}$
D) None of these
Explanation
(d)
The women choose the chairs amongst the chairs marked 1 to 4 in $\ ^{4}P_{2}$ways and the men can select the chairs from remaining in $\ ^{6}P_{3}$ ways
Total number of ways ${= \ }^{4}P_{2}{\times \ }^{6}P_{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.