There are 5 men and 5 ladies to dine at a round table.

Question:

There are 5 men and 5 ladies to dine at a round table. In how many ways can they sit so that no ladies are together?

 

Solution:

Let first arranged 5 men in the round table by 4! (By using the formula (n-1)! Mention above)

Now there are 5 gaps created between 5 men (check the figure)

So we arrange 5 ladies in this gap by $5 !$

A total number of ways to arrange 5 men and 5 ladies is $5 ! \times 4 !=2880$

 

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