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A small social network contains seven people who are network friends with six other people in the network, one person who is network friends with five other people in the network, and five people who are network friends with four other people in the network. The rest are network friends with three other people in the network. The network contains 50 pairs of network friends.
(a) How many people are network friends with three other people in the network?
(b) How many people are in the network?

Respuesta :

Answer:

(a) 11 people

(b) 24 people

Step-by-step explanation:

Part (a)

Let X be the people who are network friends with three other people in the network.

The total pairings = 50

Since [tex]v[/tex]∈[tex]V[/tex],

[tex](7)(6) + (1)(5) + (5)(4) + (X)(3) = (2)(50)[/tex]

Solve for X to find the people who are network friends with three other people,

[tex]67 + 3X = 100[/tex]

[tex]X = 11[/tex]

Answer: There are 11 people who are network friends with three other people in the network.

Part (b)

Total people in the network,

[tex]= 7 + 1 + 5 + X\\ = 13 + 11\\ = 24[/tex]

Answer: There are a total of 24 people in the network.

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