There are 6 ladies and 4 gents to dine at a round table. In how many ways can they seat themselves so that no two gents are seated together. Choose the correct answer
A) 85400  B) 36400  C) 86400  D) 14400  E) 88600
First arrange the ladies. This is a circular arrangment. 6 Gents can be arranged in 5! ways.   Now there are 6 spaces (space in between two ladies) and we have to seat 5 gents there.   First select 4 places out of 5 available places. can be done in 5C4ways. Then arrange 5 gents there in 5! ways.   Total: 5!*5C4*4! = 14400   14400 is the answer.
<result>D</result>
There are 6 ladies and 4 gents to dine at a round table. In how many ways can they seat themselves so that no two gents are seated together.