(Solution) - The qualified applicant pool for six management trainee positions consists -(2025 Original AI-Free Solution)

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The qualified applicant pool for six management trainee positions consists of seven women and five men.
(a) How many different groups of applicants can be selected for the positions?
(b) How many different groups of trainees would consist entirely of women?
(c) Probability Extension If the applicants are equally qualified and the trainee positions are selected by drawing the names at random so that all groups of six are equally likely, what is the probability that the trainee class will consist entirely of women?