In: Statistics and Probability
Suppose a committee wants to decide the service award for last year. There are a total of 6 candidates, Alice, Brigitte, Chris, Dave, Emma, and Frank. Among the six candidates, Alice, Brigitte, and Emma are females and the rest three are males. The committee must decide exactly three people to be awarded, and the nominations must meet all of the following criteria. At least one female must be nominated; Chris and Emma cannot be both nominated; Since Alice and Brigitte work together all the time last year, if one of them is nominated, so is the other; Exactly one of the two people Chris and Dave will be nominated; The nomination cannot be a list containing exactly Alice, Brigitte, and Chris; If Chris cannot get the nomination, neither can Brigitte. Now, as the chair of the committee, how do you decide the nominations?