Question

A group of four people is said to be “interesting", if there are at most five...

A group of four people is said to be “interesting", if there are at most five pairs who are friends. Assume that each pair of people are friends, independent of every other pair, with probability 1/2 . Let S be the number of pairs that are friends in this group.

Question : What is the probability that a randomly chosen group of four people is “interesting"?

Question : if 128 different people observe randomly chosen groups of four people, how many times on average do these observations lead to the conclusion that the society is interesting?

my way of thought is the following and its wrong, for me there are 6 pairs in this group of 4 persons. ( 4 c 2). Then i Calculate the at most till 5 pairs. that is I sum from 1 to 5, with the combin value and probability. but its wrong, can you help please?

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