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Question

In how many ways n books can be arranged in a row so that two specified books are not together

A
n!(n2)!
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B
(n1)!(n2)
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C
n!2(n1)!
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D
(n2)n!
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Solution

The correct option is C n!2(n1)!
The total no: of arrangement in which all n books can be arranged on the shelf without any condition is
nPn=n! ...... (i)
The books can be together in 2P2=2!=2 ways.
Consider these two books which are kept together as one composite book and with the rest of the (n2) books from(n1) books which are to be arranged on the shelf then the no: of ways=n1Pn1=(n1)!
Hence by the fundamental principle , the no: of ways on which the two particular books are together =2(n1)! ........ (ii)
The no: of ways n nooks on a shelf so that two particular books are not together is (i)(ii)
=n!2(n1)!

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