Fourteen points are placed on the circumference of a circle. Two of these fourteen points are coloured blue; four are coloured green and the other eight red. How many quadrilaterals are there such that all their vertices are points from this set of twelve points and each of the quadrilaterals has at least one vertex of each colour?
Sep 18th 2005, 04:31 AM
Firstly note that a quadrilateral is determined by its (unordered) set of vertices.
There are three cases: the vertex colours could be RRBG, RBBG or RBGG (in some order). Take RRBG as an example. You need to count the number of ways of choosing 2 red out of 8, 1 blue out of 2 and 1 green out of 4. The other two cases follow similarly.