Suppose you have 10 points in the plane with no three collinear.
(a) How many different line segments are formed by joining pairs of of these points?
(b) How many different triangles are formed by these line segments?
(c) If A is one of the 10 points, how many of the triangles formed by the line segments have A as a vertex?
+128475 (a) How many different line segments are formed by joining pairs of of these points?
I don't know the answers to (b) or (c) but for this one we have
n ( n -1) 10 * 9
________ = _______ = 45
2 2
See here for a simple derivation of the formula :
https://www.basic-mathematics.com/number-of-segments.html
