Question

Three persons are said to form a Triangle if all of them know each other or none of themknow each other. Six persons are chosen from a population. What is the minimum number ofTriangles that can be found among these six persons?​

Answer 1

Three persons are said to form a Triangle if all of them know each other or none of them know each other.

From given we have,

3 person form a triangle.

6 persons are chosen from a population.

The minimum number of triangles that can be found among these six persons are:

Let the names of 6 persons be, a, b, c, d, e and f.

Since the vertices of a triangle are 3, so the minimum number of triangles that can be found among these six persons is 2

Δ abc and Δ def.

Maximum number of triangles that can be found among these six persons is 9.

Δ abc, Δ abd, Δ abe, Δ abf, Δ acd, Δ ace, Δ acf, Δ ade, Δ adf