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28
Good question. This is an 'analogue' of this puzzle: "Eight people meet for the first time. If they each shake hands with everyone else, how many handshakes are there?" There is a formula, but who would remember it?
Imagine you and I are both among the eight people. You would shake hands with seven others. I would say the same thing, and so could each of the others.
That gives 8x7 = 56, but you and I both counted the time we shook hands with one another , in fact each handshake is counted twice. The number of handshakes is actually 56/2 = 28.
This can be generalized to say that the number of ways to choose 2 objects from a group of n objects is n(n-1)/2.
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How many line can contain 3 non collinear points?
Two intersecting lines can always cover three non-collinear points.
How many different lines are determined by 3 non collinear points?
Any three non-collinear points will define a single plane. A plane is composed of an infinite number of distinct lines.
How many different lines can be formed by three non-collinear points?
Three
What is a non collinear lines?
the lines which are not parallel to each other are non collinear lines
How many lines can be drawn through 5 non collinear points?
Through any two distinct points, exactly one line can be drawn. For 5 non-collinear points, each pair of points can form a line. The number of ways to choose 2 points from 5 is given by the combination formula ( \binom{5}{2} ), which equals 10. Therefore, 10 lines can be drawn through 5 non-collinear points.
