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# help

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There are 5 red, 4 green and 3 blue points on a circle. Find the number of those line segments which have end points of different colors.

Mar 13, 2020

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Each line segment from a red point that goes to either a green point or a blue point has endpoints of different colors.

There are 7 segments from each red point and there are 5 red points, for a total of 35 segments.

Each line segment from a green point that goes to either a red point or a blue point has endpoints of different colors.

There are 8 segments from each green point and there are 4 green points, for a total of 32 segments.

Each line segment from a blue point that goes to either a green point or a red point has endpoints of different colors.

There are 9 segments from each blue point and there are 5 blue points, for a total of 27 segments.

Adding these together, we get 35 + 32+ 27 = 94 segments.

However, we have counted each segment twice, so we need to divide that answer by 2:  47 segments.

Mar 14, 2020