MathematicsThe number of ways in which 7 persons can be seated at a round table if two particular persons are not to sit together, is :

The number of ways in which $7$ persons can be seated at a round table if two particular persons are not to sit together, is :

A
$120$
B
$480$
C
$600$
D
$720$

Solution:

The number of arrangement of 7 People around a circle $= (n - 1)! = (7 - 1)! = 6! = 720$
let $M_{1}$ and be two $M_{2}$ Particular $M_{1} & M_{2}$ .
Remaining, $5$ person.
Number of arrangement of $5$ person $= 5! = 120$ ways $\times 2! (2$ people arrange) $= 240$ ways
Required number of arrangement $= 720 - 240 = 480$

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