Seven of 12 employees of a corporation are men. Suppose that 4 employees are
selected at random as delegates for a conference.
That's 7 men employees plus 5 women employees = 12 employees
How many selections will contain:
a) exactly 3 men?
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
C) what is the probability that a random selection will contain exactly 3 men?
That's 175 ways (from part a) out of (12 choose 4) = 175/(12C4) =
175/495 = 35/99
Edwin