VN-TST 1997 Problem 6

Let $n$ , $k$ , $p$ be positive integers with $2 \le k \le \frac {n}{p + 1}$ . Let $n$ distinct points on a circle be given. These points are colored blue and red so that exactly $k$ points are blue and, on each arc determined by two consecutive blue points in clockwise direction, there are at least $p$ red points. How many such colorings are there?