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Question

Ten different books are arranged on a shelf. Find the number of different ways in which this can be done, if 2 specified books are:1) not to be together 2) to be together

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Solution

There are total 10 books .So total arrangement when there is no restriction = 10!Now we wil take two book together and consider them as 1 so total number of arrangemnet of these 9 books=9!But 2 books considered as one can also interchange their position so, total number of ways = 9!×2!Now when two books are not together then total number of ways = 10!-9!×2!

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