The qualified applicant pool for three management trainee positions consists of

Question

The qualified applicant pool for three management trainee positions consists of seven women and four men. (a) How many different groups of applicants can be selected for the positions? many diff would co entirely of af women? (c) Probabuity 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 equaly likely, what is the probability that the trainee class will consist entirely of women? (Round your answer to four decimal places.) equally quali ted and the trainee posnor s are moed bydrawing the names at ranom so that a" voups of three are equal, like y, what ste pooablity that metranee dass w·consist entirely of are

Explanation / Answer

It is given that the qualified applicant pool for 3 management trainee positions consists of 7 women and 4 men.

So, in total there are 7+4=11 applicants.

We use combinations to solve the abive question.

(a) The number of different group of applicants that can we selected for the postions is given by the combination 11C3. This is equivalent to saying the number of ways in which three people can be selected from a group of 11 people. So, 11C3 = 165 different groups can be selected for the positions.

(b) The number of distinct groups of trainees consisting entirely of women can be selected in 7C3 ways. this is equivalent to saying that we select the group of 3 trainees only from the women applicants. So, 7C3=35 different groups consisting entirely of women can be selected.

(c)Now the probability of the trainee class consisting entirely of women is given by dividing the number of favourable cases by the total number of possible cases which is the figure obtained in (b) divided by the figure obtained in (a). Thus, we have P(The trainee class consists entirely of women)=35/165=7/33=0.2121.

In the second case it is given that there are 14 qualified applicants for 8 trainee positions in a fast food management program. So, the number of different groups of trainees that can be selected is given by the combination 14C8 = 3003.

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