Question

The qualified applicant pool for three management trainee positions consists of eight women and four 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 three are equally likely, what is the probability that the trainee class will consist entirely of women? (Round your answer to four decimal places.)

Answer 1

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Answer:

The number of women’s is 8

The number of men’s is 4

The total number of members is: 8 + 4 = 12

A.

Only 3 trainees are available

Different groups = Selecting random 3 from 12 members =  12C3 = 220

B.

Only 3 trainees are available

Different groups = Selecting random 3 from 8 women = 56

C.

Probabiliy that all are women=8C3/12C3=56/220=0.254545