4 gentlemen and 4 ladies take seats at random around a table. The probability that they are sitting alternately is:

 Given,

4 gentlemen and 4 ladies take the seats at the random round table.

Let us consider, the gentlemen take the seats first. It can be done in (4 – 1)! ways

(4-1)! = 3! = 6 ways

Now, the ladies will be sitting in the 4 gaps in 4! ways 

4! = 4.3.2.1 = 24 ways

Thus, the total number of ways when ladies and gentlemen can sit alternatively is: 6 x 24 = 144 ways

Hence, the probability will be: 144/(8-1)! = 144/7! = 1/35