Q. The number of ways in which 5 ladies and 7 gentlemen can be seated in a round table so that no two ladies sit together, is
A) $\frac{7}{2}(720)^{2}$
B) $7(360)^{2}$
C) $7(720)^{2}$
D) 720
Explanation
(a)
First we fix the alternate position of 7 gentlemen in a round table by $6!$ ways.
There are seven positions between the gentlemen in which 5 ladies can be seated in $\ ^{7}P_{5}$ ways
$\therefore$ required number of ways
$= 6! \times \frac{7!}{2!} = \frac{7}{2}(720)^{2}$
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Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.