Q. Eight chair 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 chair marked 1 to 4; and then the men select the chairs from amongst the remaining. The number of possible arrangement is
A) $\ ^{6}C_{3} \times {\ ^{4}C}_{2}$
B) $\ ^{4}P_{2} \times {\ ^{6}P}_{3}$
C) $\ ^{4}C_{2} + {\ ^{4}P}_{3}$
D) None of these
Explanation
(b)
Since, first the 2 women select the chairs amongst 1 to 4 in $\ ^{4}P_{2}$ ways.
Now, from the remaining 6 chairs three men could be arranged in $\ ^{6}P_{3}$ ways.
$\therefore$ Total number of arrangements$= \ ^{4}P_{2} \times \ ^{6}P_{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.