Probability question

Question

Quen: Given a set of 15 points in a plane, how many lines would necessary to connect all possible pairs of points?

Answer 1

Number the points 1 .. 15

Then from point 1 there will be 14 lines (to 2, 3 .... 15)

From point 2 there will be 13 more lines (line to 1 is already drawn)

From point 3 , 12 more lines ...

... From point 14, 1 more line

So total 1 + 2 + 3 + ... + 14 = (14 x 15)/2 = 7 x 15 = 105 lines