Question

The complexity of interpersonal relationships increases dramatically as the size of a group increases. Determine the numbers of different two-person relationships in groups of people of sizes (a) 3, (b) 8, (c) 12, and (d) 20.

Answer 1

(a) 3

(b) 28

(c) 66

(d) 190

Explanation:

For any group of people of size 'n' people, the number of different two-person relationships, if order does not matter, is given by:

`N=(n!)/((n-2)!2!)`

(a) For n = 3

`N=(3!)/((3-2)!2!)=3`

(b) For n = 8

`N=(8!)/((8-2)!2!) = 28`

(c) For n = 12

`N=(12!)/((12-2)!2!)=66`

(d) For n =20

`N=(20!)/((20-2)!2!) =190`