There are 6 ladies and 3 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 most appropriate option:
A) 8540  B) 2880  C) 8640  D) 6560  E) 8860
First arrange the ladies. This is a circular arrangment. 6 Gents can be arranged in 5! ways.   Now there are 4 spaces (space in between two ladies) and we have to seat 3 gents there.   First select 3 places out of 4 available places. can be done in 4C3 ways. Then arrange 3 gents there in 3! ways.   Total: 5!*4C3*3! = 2880   2880 is the answer.
<result>B</result>
There are 6 ladies and 3 gents to dine at a round table. In how many ways can they seat themselves so that no two gents are seated together.