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In a school there are 20 students, one teacher and one principal. In how many ways can these people sit in a round table such that the principal sits in between the teacher and a student?

In a school there are 20 students, one teacher and one principal. In how many ways can these people sit in a round table such that the principal sits in between the teacher and a student? Correct Answer 2 × 20!

Number of students = 20

Let us consider the principal and teacher as one unit

⇒ Number of people = 21

In a circular arrangement n people can be seated in (n - 1)! ways

⇒ Number of ways in which 21 people can be seated = (21 - 1)! = 20!

Also, the principal and teacher can sit in 2 different ways

⇒ Total ways = 2 × number of ways in which 21 people can sit

∴ Total ways = 2 × 20!

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