SOLUTION: One factory employs 35 male and 20 female workers. The factory owner wanted to form A social committee for male and female workers with 5 randomly selected members: What is the pr

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Question 1207831: One factory employs 35 male and 20 female workers. The factory owner wanted to form A social committee for male and female workers with 5 randomly selected members: What is the probability that the chairman of the committee , Vice-Chairman of the Committee and the treasurer are male workers, and the other members are from female Workers?

Answer by ikleyn(52797) About Me  (Show Source):
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One factory employs 35 male and 20 female workers. The factory owner wanted to form
a social committee for male and female workers with 5 randomly selected members:
What is the probability that the chairman of the committee,
Vice-Chairman of the Committee and the treasurer are male workers,
and the other members are from female Workers?
~~~~~~~~~~~~~~~~~~~~~~~~ 

Total set consists of 35 + 20 = 55 persons.


    P = %2835%2F55%29%2A%2834%2F54%29%2A%2833%2F53%29%2A%2820%2F52%29%2A%2819%2F51%29 = 0.03575  (rounded).    ANSWER


The meaning of this formula is clear from its structure.


Factor  35%2F55  is the probability that at first selection the chairman is a male worker.

Factor  34%2F54  is the probability that at second selection the vice-chairman is a male worker.

Factor  33%2F53  is the probability that at third selection the treasurer is a male worker.

Factors  20%2F52  and  19%2F51  are the probabilities that at fourth and fifth selections the members are female workers.


Another possible expression/formula is

    P = %28C%5B35%5D%5E3%2AC%5B20%5D%5E2%29%2FC%5B55%5D%5E5

with the use of combinations.


Both formulas are formally equivalent and produce the same value of the probability as the answer.


    For completeness of explanation, notice that in this problem there is the set of three positions 
    for male workers and another set of two positions for female workers.

    But the order of males in their set of positions does not matter, 
    as well as the order of female workers in their set of positions does not matter, too.

    Therefore, this problem can be treated in terms of combinations.

Solved.