SOLUTION: how many collinear points are there containing 153 segments? how many rays are there containing 15 collinear points? Please help me to answer this with a little bit solution thank

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Question 1085988: how many collinear points are there containing 153 segments?
how many rays are there containing 15 collinear points? Please help me to answer this with a little bit solution thank you very much
Answer by ikleyn(52911) About Me  (Show Source):
You can put this solution on YOUR website!
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1. how many collinear points are there containing 153 segments? 

Answer.  18 points.   

         Because %2818%2A17%29%2F2 = 153.

         Or, in other words, because C%5B18%5D%5E2 = %2818%2A%2818-1%29%29%2F2 = 153.

         Or, in other words, because the number of combinations of 18 points taken 2 at a time is 153.


         Or, you can solve this equation for n: %28n%2A%28n-1%29%29%2F2 = 153 and to get n = 18.

Every two point of your collection define a segment, and, reversely, each segment is defined by two points of the collection.

Therefore, there is one-to-one correspondence between the segments and (unordered) pairs of points.