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Physics Guru is an online education and competitive examinations preparation portal founded by Manish Verma, an IIT Madras alumnus, providing learning resources for competitive examinations.

The emphasis is on conceptual understanding, analytical thinking and problem solving rather than simply memorising formulas and standard methods.

The objective is to help students understand what they are learning and develop the ability to solve problems they have not seen before.

Circular Permutations ~ 3 Boys & 3 Girls

In how many ways can 3 boys and 3 girls be seated at a round table such that exactly 2 boys sit together?

Solution

Circular permutations without any restriction = (6 - 1)! = 120

Circular permutations when no 2 boys are together which is B G B G B G situation is a circle = 2! $\times$ 3! = 12

Circular permutations when all the 3 boys are together = (4 - 1)! $\times $ 3! = 36

Circular permutations for exactly 2 boys sitting together =  120 - (12 + 36) = 72