There are 6 gentlemen and 3 ladies to dine at a round table. In how many ways can they seat themselves so that no two ladies are seated together.
Select.
A) 8540
B) 3640
C) 2880
D) 3880
E) 88600
First arrange the Gents. This is a circular arrangment. 6 Gents can be arranged in 5! ways.   Now there are 4 spaces (space in between two gents) and we have to seat 3 ladies there.   First select 3 places out of 4 available places. can be done in 4C3ways. Then arrange 3 ladies there in 3! ways.   Total: 5!*428803*3! = 2880   2880 is the answer.
<result>C</result>
There are 6 gentlemen and 3 ladies to dine at a round table. In how many ways can they seat themselves so that no two ladies are seated together.