If n objects are arranged in a row,then the n | vedclass

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(A) To select $3$ objects from $n$ objects arranged in a row such that no two are consecutive,we use the gap method.Let the $n-3$ objects that are not

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${}^{n - 2}{C_3}$

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(A) To select $3$ objects from $n$ objects arranged in a row such that no two are consecutive,we use the gap method.Let the $n-3$ objects that are not selected be represented by $X$.$X \_ X \_ X \_ \dots \_ X$There are $n-3$ objects,which create $(n-3) + 1 = n-2$ available gaps (including the ends).We need to choose $3$ gaps out of these $n-2$ gaps to place the selected objects.The number of ways to do this is given by the combination formula ${}^{n-2}C_3$.

If $n$ objects are arranged in a row,then the number of ways of selecting three of these objects such that no two of them are next to each other is:

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