The number of ways in which seven persons can be arranged at a round table if two particular persons may not sit together, is

# The number of ways in which seven persons can be arranged at a round table if two particular persons may not sit together, is

1. A

480

2. B

120

3. C

80

4. D

none of these

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### Solution:

Excluding the two particular persons, t! remaining five persons can be arranged at the round table in = 24 ways. Now, there are 5 gaps between them in ever .arrangement and the two particular persons can be arran;;: h1 these 5 gaps in ${5}_{{p}_{2}}$ ,ways.

So, the required number of ways $=24{×}^{5}{P}_{2}=480$

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