Question

ten distinct points are chosen on a circle. a line segment is drawn between every pair of chosen points. how many line segments are drawn?

Answer 1

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.