you can count them if you like...
Probability
Level
3
Consider 25 straight lines in a plane of which no 2 are parallel and no 3 are concurrent. How many intersection points are there?
This problem is inspired by this problem.
The answer is 300.
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1 solution
As no 2 lines are parallel & no 3 or more are concurrent, we are going to get distinct intersection points joining every 2 lines. Thus, from 25 Lines, we can select two lines in (25 C 2) = 300 ways. So, there are exactly 300 intersection points. The problem will become a bit complicated, if there was mentioned about some lines to be parallel or concurrent. Then, we had to subtract something from this answer but no such thing is mentioned. So, 300 is the answer.