Chapter 8.5, Problem 70E

(a)

To determine

To find: the number of different two person relationships that are possible in groups of people of sizes 3.

Answer to Problem 70E

Number of ways selection two out of three person relationship is 3.

Explanation of Solution

Given Information:

The number of possible interpersonal relationships increases dramatically as the size of a group increases.

Calculation:

Two of three person relationship

  ${}_3{C}_2=\frac{3!}{\left(3-2\right)!2!}=3$

Hence number of ways selection two out of three person relationship is 3.

(b)

To determine

To find: the number of different two person relationships that are possible in groups of people of sizes 8.

Answer to Problem 70E

Number of ways selection two out of eight person relationship is 28.

Explanation of Solution

Given Information:

The number of possible interpersonal relationships increases dramatically as the size of a group increases.

Calculation:

Two of eight person relationship

  ${}_8{C}_2=\frac{8!}{\left(8-2\right)!2!}=28$

Hence number of ways selection two out of eight person relationship is 28.

(c)

To determine

To find: the number of different two person relationships that are possible in groups of people of sizes 12.

Answer to Problem 70E

Number of ways selection two out of twelve person relationship is 66.

Explanation of Solution

Given Information:

The number of possible interpersonal relationships increases dramatically as the size of a group increases.

Calculation:

Two of twelve person relationship

  ${}_{12}{C}_2=\frac{12!}{\left(12-2\right)!2!}=66$

Hence number of ways selection two out of twelve person relationship is 66.