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

Vedclass · Accepted Answer

${}^{n-2}C_3$

Vedclass · Answer

(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 $X$. These $n-3$ objects create $n-2$ possible gaps (including the ends) where the $3$ selected objects can be placed.These gaps are represented as: $\_ X \_ X \_ X \_ ... \_ X \_$.The number of gaps available is $(n-3) + 1 = n-2$.We need to choose $3$ gaps out of these $n-2$ gaps to place the $3$ objects.Therefore,the number of ways is ${}^{n-2}C_3$.

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

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