## Problem based on concepts of Triangles as well as probability

Hello all, Can someone help in solving this problem? Suppose M is a set of triangles formed by using sides of lengths 1,2,4 & 7 units: whatis the probability that a triangle at random from set will be equilateral? This involves the concepts of both Proability and triangles as well. Thanks in advance.

## Equilateral triangles:

Number of possible equilateral triangles = 4

Letâ€™s find number of triangles with 2 equal sides
Let the equal sides be 1 : other side cant be 4 or 7 (Sum of two sides should more than or equal to the third side) , number of possible triangles = 1
If the equal sides are 2 : 7 cant be the third side, So total number of triangles = 2
If the equal sides are 4 â€“ number of triangles = 3
If the equal sides are 7 â€“ number of triangles = 3
So total number of bilateral triangles are = 9
Finally we will try to find the number of triangles with all different sides
7 canâ€™t be the side of any of the triangle. (The other two large sides 2 + 4 < 7)
And we cant have any triangle with 1, 2, 4
So the total number of triangles = 13.
Thus the probability that one of the triangles is equilateral is 4/13