Question: Topic of counting: double counting, k-to-1 functions, binomial and multinomial coefficients, counting poker hands (I just need help with part c) 2. Let K5 denote

Topic of counting: double counting, k-to-1 functions, binomial and multinomial coefficients, counting poker hands (I just need help with part c)

2. Let K5 denote the complete graph on 6 vertices (that is, there is an edge between every pair of vertices). A triangle is a set of three vertices that are all connected to each other. A set of two edges that share a vertex is called an incident pair (i.p.). The shared vertex is called the center of the i.p. For example, {(av), (vw is an i.p. where am, and w are distinct vertices and v is the center. Now suppose every edge is colored red or blue. A triangle or i.p. is called multicolored when its edges are not all the same color. (c) Consider the mapping from incident pairs to triangles we get by adding the "third\" edge: {Gt-v), (ti-110} '-> {t-v), (II-w}, (it-W} Note that multicolored i.p.s map to multicolored triangles. Show that this mapping is 2-to1 on multicolored objects. a..- - _

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