Suppose that 5 female applicants and 5 male applicants are available to fill fou

Question

Suppose that 5 female applicants and 5 male applicants are available to fill four different job positions, job I, job II, job III, and job IV (each job position only needs one person). If a manager is randomly selecting people to fill these different job positions, what is the probability that for jobs I and II the manager selects a female, and for jobs III and IV the manager selects a male? (You must show your calculation steps to earn credits. Any answer with no work will receive zero credit.)

Explanation / Answer

Total number of applicants = 10

No of jobs = 4

Total possible arrangements = 10P4 = 10x9x8x7 = 5040

No of ways in which 2 females can be selected for jobs I and II= 5P2 = 30

No of ways in which two males can be selected for jobs III and IV = 30

So, total no of ways I which candidates can be selected =30x30 = 900

So, the probability that a female is selceted for jobs I and II and a male is selected for jobs III and IV = 900/5040

= 0.1786

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