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
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Maths