There are 6 gentlemen and 5 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 option:  A) 85400  B) 36400  C) 86400  D) 65600  E) 88600
6 men can be arranged around a table in (6-1)= 
<gadget id="calculator">(6-1)</gadget>
<output>5</output>
5! ways.   Now, if we place each woman between the men then no two women will be together. There are 6 available slots between the men, thus 6C5=6 is the number of ways we can choose 5 slots out of 6 for the women.   Next, these 5 women can be arranged in 5! ways, hence the total number of ways is 5!*6*5!=86,400.   Answer: 86400.
<result>C</result>
There are 6 gentlemen and 5 ladies to dine at a round table. In how many ways can they seat themselves so that no two ladies are seated together.