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Colors of points on a circle

Source: Vietnam TST 1997, Problem 6

July 28, 2008
combinatorics unsolvedcombinatorics

Problem Statement

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