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The qualified applicant pool for three management trainee positions consists of seven women and six 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.)

Respuesta :

adelekeademolu

Answer:

(a) 286

(b) 35

(c) 0.1224

Step-by-step explanation:

(a) There are a total of 7 + 6 = 13 people to choose 3 from. The number of ways this can be done is given by

[tex]\binom{13}{3} = 286[/tex]

(b) If the selection were to consist of only women, then it will be from the 7 women only. The number of ways is then

[tex]\binom{7}{3} = 35[/tex]

(c) Any selection of 3 people is equally likely and each candidate is equally qualified. The sample space is space is equiprobable. The probability of selecting only women is

[tex]\dfrac{\text{Number of ways of selecting only women}}{\text{Total number of ways of selecting}}=\dfrac{35}{286}=0.1224[/tex]

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