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  4. Seven persons are to be seated in a row. The probability that two particular persons sit next to each other, is

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Q. Seven persons are to be seated in a row. The probability that two particular persons sit next to each other, is

Probability

Solution:

Given, number of persons $=7$
Now, treating the two persons as one, we have 6 persons.
Total number of sitting arrangements $=7$ !
Favourable number of arrangements $=6$ !
2 persons can be arranged in two ways.
Total number of favourable arrangments $=2(6 !)$
$\therefore$ Required probability $=\frac{2(6 !)}{7 !}=\frac{2}{7}$