  This article studies the number of ways of selecting $k$ objects arranged in
$p$ circles of sizes $n_1,\ldots,n_p$ such that no two selected ones have less
than $s$ objects between them. If $n_i\geq sk+1$ for all $1\leq i \leq p$, this
number is shown to be
$\frac{n_1+\ldots+n_p}{k}\binom{n_1+\ldots+n_p-sk-1}{k-1}$. A combinatorial
proof of this claim is provided, and some nice combinatorial formulas are
derived.
