Question

prove that total number of ways of selection of r points out of n points in a row such that no two of them are consecutive C(n-r+1,r).

Answer 1

Here, the total number of points is `n` and we have to select `r` points.
So, the points left will be `n-r`.
Between the remaining `n-r` points, there are total `n-r+1` places where we can select `r` points
such that two points are consecutive.
So, the number of ways doing this ` = C(n-r+1),r)`.