The number of ways in which n books can be arranged on a shelf so that two particular books shall not be together is

(n - 2) (n - 1)!

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(n - 1) n!

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(n - 2) n!

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None of these

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Solution

The correct option is A $(n - 2) (n - 1)!$
No. of ways that no. $2$ books are together $=$ Total ways $-$ No. of ways $2$ books are together
$= n! - (n - 1)! 2!$
$= (n - 2) (n - 1)!$

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The number of ways in which n books can be arranged on a shelf so that two particular books shall not be together is

The correct option is A (n−2)(n−1)!No. of ways that no. 2 books are together = Total ways − No. of ways 2 books are together =n!−(n−1)!2! =(n−2)(n−1)!

The correct option is A $(n - 2) (n - 1)!$
No. of ways that no. $2$ books are together $=$ Total ways $-$ No. of ways $2$ books are together
$= n! - (n - 1)! 2!$
$= (n - 2) (n - 1)!$