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.
What is the probability that a randomly chosen group of four people 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 combined value and probability. But it is wrong, can you help please?