Problem Solving

In a room filled with 7 people, 4 people have exactly 1 friend in the room and 3 people have exactly 2 friends in the room (Assuming that friendship is a mutual relationship, i.e. if John is Peter's friend, Peter is John's friend). If two individuals are selected from the room at random, what is the probability that those two individuals are NOT friends?

A. 5/21
B. 3/7
C. 4/7
D. 5/7
E.16/21

4/7 probability of choosing one of the 4 people who have 1 friend
1/6 probability of choosing that friend

3/7 probability of choosing one of the 3 people who have 2 friends
2/6 probability of choosing one of the friend


(4/7 * 1/6 + 3/7*2/6) = 5/21

1-5/21 = 16/21

You can make it with a graph, one circle per person and lines to represent friendship. You will fastly sum the number of non friend couples that you divide by 7C2