9303753286127016 4 gentlemen and 4 ladies take seats at random around a table. The probability that they are sitting alternately is:

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

Balkishan Agrawal

At the helm of GMS Learning is Principal Balkishan Agrawal, a dedicated and experienced educationist. Under his able guidance, our school has flourished academically and has achieved remarkable milestones in various fields. Principal Agrawal’s vision for the school is centered on providing a nurturing environment where every student can thrive, learn, and grow.

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