Question 1132287
Seven of 12 employees of a corporation are men. Suppose that 4 employees are
selected at random as delegates for a conference. 
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That's 7 men employees plus 5 women employees = 12 employees
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How many selections will contain:

a) exactly 3 men?
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That's 3 men and 1 woman.

(7 men CHOOSE 3)∙(5 women CHOOSE 1) = (7C3)∙(5C1) = (35)∙(5) = 175  

b) at least 3 men? 

That's the number with exactly 3 men PLUS the number with exactly 4 men.

We have already found that the number with exactly 3 men is 175.
So we need to add the number with exactly 4 men (and no women).

175 + (7 men CHOOSE 4) = 175 + 35 = 210 
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C) what is the probability that a random selection will contain exactly 3 men?
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That's 175 ways (from part a) out of (12 choose 4) = 175/(12C4) = 
175/495 = 35/99

Edwin</pre>