SOLUTION: 5 of 10 employees of a corporation are men . Suppose that 4 employees are selected at random as delegates for a conference.how many selections will contain : a) exacrly 3 men ? B)

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Question 1132285: 5 of 10 employees of a corporation are men . Suppose that 4 employees are selected at random as delegates for a conference.how many selections will contain : a) exacrly 3 men ? B) at least 3 men ? C) what is the probability that a random selection will contain exactly 3 men ?
Answer by ikleyn(52852) About Me  (Show Source):
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a)   exactly 3 men ? 
    (select 3 of 5 men) * (select 1 of 5 women) = C%5B5%5D%5E3.C%5B5%5D%5E1 = %285%2A4%29%2F%281%2A2%29.5 = 10*5 = 50 different selections.

b)   at least 3 men ? 
    (select 3 of 5 men) * (select 1 of 5 women) + (select 4 of 5 men) = C%5B5%5D%5E3.C%5B5%5D%5E1 + C%5B5%5D%5E4 = 50 + 5 = 55 different selections.

c)   what is the probability that a random selection will contain exactly 3 men ? 
    P = %28C%5B5%5D%5E3%2AC%5B5%5D%5E1%29%2FC%5B10%5D%5E4 = %28%2810%2A5%29%29%2F%28%28%2810%2A9%2A8%2A7%29%2F%281%2A2%2A3%2A4%29%29%29 = 50%2F210 = 5%2F21 = 0.2381 = 23.81% (approximately).