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Q.

The number of ways of arranging 9 persons around a circle if there are two other persons between two particular persons is

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a

3×7!

b

4×7!

c

2×(7!)

d

9×8P2

answer is A.

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Detailed Solution

Out of persons

Let A, B be two particular persons.

A,P1,P2 B           A P2,P1 B

Two persons from 7 persons (other than A, B) can be selected in 7C2 ways.

Along with 4 people including A, B remaining 5 persons can be arranged around a table in (6-1)! Ways.

Two persons between A, B can be arranged in 2 ways. A, B can be re arranged in 2 ways

∴  Required =7C2 × 5! × 2 × 2

                  =2(7!)

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