There are 6 gentlemen and 4 ladies to dine at a round table. In how many ways can they seat themselves so that no two ladies are seated together.	Choose the correct choice from the following answers.
A) 14400
B) 36400
C) 86400
D) 65600
E) 88600
First arrange the Gents. This is a circular arrangment. 6 Gents can be arranged in 5! ways.   Now there are5 spaces (space in between two gents) and we have to seat 4 ladies there.   First select 4 places out of 5 available places. can be done in 5C4 ways. Then arrange 4 Ladiess there in 4! ways.   Total: 5!*5C4*4! = 14400   14400 is the answer.
<result>A</result>
There are 6 gentlemen and 4 ladies to dine at a round table. In how many ways can they seat themselves so that no two ladies are seated together.