Question 1013066: The question is:
15 points lie around a circle. Each point is connected to every other point by a straight line. How many lines are formed in this way?
I don't understand why the answer is 105. Shouldn't it be 14 factorial (14!) because if you think about the first point connecting it to 14 other points, then the next point 13 (because one of the paths is counted in that 14 previously) etc...
Please help
Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website! You have 15 points that are connected with 14 other points with a straight line.
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Notice the problem doesn't say that each point reaches out to touch every other point, it says each point is connected to every other point. This means that if I have two points connected by a line, A and B, I only need one line to connect the points.
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So, for every point to reach out to every other point you'd need:
15*14= 210 lines
But as I said, once you connect two points with one line, well, they are connected. So you only need:
210/2= 105
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