Question 1075774: Three hundred people apply for three jobs. Sixty of the applicants are women.
(a) If three people are selected at random, what is the probability that all are women? (Round your answer to six decimal places.)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the probability that the first applicant will be a woman is 60/300.
assuming the first is a woman, then the probability that the second will be a woman is 59/299.
assuming the second is a woman, then the probability that the third will be a woman is 58/298.
the probability that they will all be women is therefore 60/300 * 59/299 * 58/298.
this becomes equal to .0076810846
alternately this can be viewed as the number of ways you can get 3 women out of 60 divided by the number of ways you can get 3 people out of 300.
that would be c(60,3) / c(300,3) = .0076810846.
c(60,3) = 60! / (3! * 57!)
c(300,3) = 300! / (3! * 297!)
in general, c(n,x) = n! / (x! * (n-x)!)
the calculator i used is the ti-84 plus.
it can do c(300,3) but it can't do 300! / (3! * 297!).
for whatever the reasons, the combination formula works but the equivalent factorial formula doesn't work.
it has to do with internal storage requirements in the calculator.
300! is just too large for it to handle.
i used excel as well but that can't handle it either.
surprisingly, both excel and the ti-84 could handle c(300,3).
bottom line is the results are accurate but if you try to duplicate c(300,3) by using the equivalent formula of 300! / (3! * 297!) you will have difficulty.
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