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

A
480
B
120
C
80
D
none of these

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 $= 24 \times^{5} P_{2} = 480$

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