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Q.

Let Pn denotes the number of ways in which three people can be selected out of n people sitting in a row, if no two of them are consecutive. If, Pn+1−Pn=15 then the value of n is ____________ .

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answer is 8.

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Detailed Solution

Here   Pn=n−2C3 and Pn+1=n−1C3Hence,  n−1C3−n−2C3=15or  n−2C3+n−2C2−n−2C3=15or  n−2C2=15 cut n=8
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