SOLUTION: the president of large company selects six employees to receive a special bonus. he claims that the six employees are chosen randomly from among the 30 employees, of whom 19 are wo

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Question 805827: the president of large company selects six employees to receive a special bonus. he claims that the six employees are chosen randomly from among the 30 employees, of whom 19 are women and 11 are men. what id the probability that no women is chosen
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If the names are taken out one by one out of a hat containing all 30 names,
and are written in order on a list, there are
30%2A29%2A28%2A27%2A26%2A25 possible lists.
With just the names of the 11 men, we can make only
11%2A10%2A9%2A8%2A7%2A6 of those lists.
As a fraction of all the possible lists, that is
11%2A10%2A9%2A8%2A7%2A6%2F%2830%2A29%2A28%2A27%2A26%2A25%29=22%2F28275
It really does not matter how the names are randomly selected.
In only 22%2F28275 of the cases there would be only males selected.
The probability is
22%2F28275= approximately0.0007781 or 0.07781%.
It can also be stated as the probability is 1%3Ax one in x.
22%2F28275=1%2Fx --> x=28275%2F22= approximately1285
There is a 1 in 1285 probability of selecting only men.