In how many ways n books can be arranged in a row so that two specified books are not together
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Let there be n books
No. of ways to arrange n books = n!
Let the two specified books be together, so we treat them as one, and we now have n-1 books
To arrange n-1 books = (n-1)!
This is the no. of arrangements when the two books are always together
No. of ways the two books are never together = Total no of ways to arrange the books - Arrangements when they are together
= n! - (n-1)! ///
= n(n-1)! - (n-1)!
= (n-1)(n-1)! ///
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