  In this paper we enumerate the number of ways of selecting $k$ objects from
$n$ objects arrayed in a line such that no two selected ones are separated by
$m-1,2m-1,...,pm-1$ objects and provide three different formulas when $m,p\geq
1$ and $n\geq pm(k-1)$. Also, we prove that the number of ways of selecting $k$
objects from $n$ objects arrayed in a circle such that no two selected ones are
separated by $m-1,2m-1,...,pm-1$ objects is given by
$\frac{n}{n-pk}\binom{n-pk}{k}$, where $m,p\geq 1$ and $n\geq mpk+1$.
