SOLUTION: five men in a company of 20 are graduates.if 3 men are picked out of the 20 at random, what is the probability that they are 1.all graduates 2.all non graduates 3.2 graduates 4

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Question 1023297: five men in a company of 20 are graduates.if 3 men are picked out of the 20 at random, what is the probability that they are
1.all graduates
2.all non graduates
3.2 graduates
4.at most 1 graduates
5. at least one graduates
6.2 non graduates

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
P%28X%29=C%283%2CX%29%2A%285%2F20%29%5EX%2A%281-5%2F20%29%5E%283-X%29
P%28X%29=C%283%2CX%29%2A%281%2F4%29%5EX%2A%283%2F4%29%5E%283-X%29
1. All graduates X=3
P%283%29=C%283%2C3%29%2A%281%2F4%29%5E3%2A%283%2F4%29%5E%283-3%29
P%283%29=1%2A%281%2F64%29%2A1
P%283%29=1%2F64
2. No graduates X=0
P%280%29=C%283%2C0%29%2A%281%2F4%29%5E0%2A%283%2F4%29%5E%283-0%29
P%280%29=1%2A1%2A%2827%2F64%29
P%280%29=27%2F64
3. Two graduates X=2
P%282%29=C%283%2C2%29%2A%281%2F4%29%5E2%2A%283%2F4%29%5E%283-2%29
P%282%29=3%2A%281%2F16%29%2A%283%2F4%29
P%282%29=9%2F64
4. At most one, X=0 and X=1
P%281%29=C%283%2C1%29%2A%281%2F4%29%5E1%2A%283%2F4%29%5E%283-1%29
P%281%29=3%2A%281%2F4%29%2A%289%2F16%29
P%281%29=27%2F64
So,
P=P%280%29%2BP%281%29
P=27%2F64%2B27%2F64
P=27%2F32
5. At least one, X=1, X=2, and X=3
P=P%281%29%2BP%282%29%2BP%283%29
P=27%2F64%2B9%2F64%2B1%2F64
P=37%2F64
6. Two non-graduates is the same as one graduate.
P%281%29=27%2F64