You need at least nine decimal places on this problem. You may want to use fractions instead. There are 8 candidates for a position. The candidates are interviewed independently by each member of a committee that has 5 people on it. A candidate will be hired if she is chosen by at least 4 members of the committee. In reality, the committee members cannot really distinguish among the candidates and just choose at random with no biases. What is the probability that a candidate will be selected with a unanimous vote (all committee members choose the same person)? 5/16 What is the probability that a candidate will be selected with only one dissenting vote (all but one committee members choose the same person)? What is the probability that a candidate will be selected?