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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.

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Answer:

(a) 3

(b) 28

(c) 66

(d) 190

Step-by-step 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:

[tex]N=\frac{n!}{(n-2)!2!}[/tex]

(a) For n = 3

[tex]N=\frac{3!}{(3-2)!2!}=3[/tex]

(b) For n = 8

[tex]N=\frac{8!}{(8-2)!2!} = 28[/tex]

(c) For n = 12

[tex]N=\frac{12!}{(12-2)!2!}=66[/tex]

(d) For n =20

[tex]N=\frac{20!}{(20-2)!2!} =190[/tex]

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