Answer:
45
Explanation:
You want to know the number of line segments that can be drawn between pairs of points in a group of 10 distinct points.
Solution
From the first point, 9 segments can be drawn.
From the second point 8 more segments can be drawn. (The segment to the first point has already been counted.)
From the third point, 7 more segments can be drawn. The total number of segments will be the sum of integers from 1 through 9:
9(10)/2 = 45
45 line segments can be drawn.
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Additional comment
This is identical to the "handshake" problem: the number of handshakes in a group of 10 people if each shakes hands with all the others.