Question

Let s be the set of sides and diagonals of a regular pentagon. A pair of elements of s are selected at random without replacement. What is the probability that the two chosen segments have the same length?

Answer 1

A regular pentagon means five sided figure which has all 5 sides equal(RED in color). Now we can draw the diagonals too, and we find there are 5 diagonals ( BLACK in color).

To count total sides is to find ways to select 2 of A, B, C, D, E, that is 5C2 = 10 segments.

So choosing equal sides means choosing two of the five RED sides = 5*4, or choosing two of the five diagonals BLACK lines = 5*4

Total ways to choose 2 sides out of 10 is 10*9

Probability = 5∗4+5∗410∗9=49