question_answer

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)         \[720\]

E)  \[360\]

Correct Answer: A

Solution :

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 \[=6!\times \frac{7!}{2!}\]                                                 \[=\frac{7}{2}{{(720)}^{2}}\]