Problem 3
Probability
Level
1
Seven points are marked on a piece of paper such that no three of them lie on a straight line. How many straight lines can be drawn to pass through any two points?
Check out the set: Combinatorics .
35
21
42
210
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1 solution
If no 3 points are collinear, then we have distinct lines between any 2 points. Each of the 7 points can be connected with the other 6 (and to handle the double counting, we have to divide our result by 2):
2 7 × 6 = 2 1