SOLUTION: Theo owns a large company and is hiring five people from an applicant pool consisting of eight men and six women. What is the probability that Theo will hire all men? Would this be

Question 1096888: Theo owns a large company and is hiring five people from an applicant pool consisting of eight men and six women. What is the probability that Theo will hire all men? Would this be unusual?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
If Theo lists the candidates in order of most qualified to least qualified,
how many possible seequences could represent the first 5 names in that list?
How many of those sequences of 5 names would only have names of men?
There are possible seequences of 5 names that can be made from the names of the applicants.
There are possible seequences of 5 names that can be made from the names of the male applicants.
As only of the possible sequences of 5 applicant names would use only names of men,
random choice would make the probability that Theo hires only men
.
That is about or about .
If the candidates are supposed to be similarly qualified for the jobs,
that would be unusual.

NOTES:
A teacher may insist in figuring out number of possible sets instead of lists of candidates,
for total sets and for men-only sets.
However, common sense and math tell you that the result of the calculation would be the same.
A teacher may want you to use the symbols, vocabulary words (such as permutations, combinations, factorials), and "formulas" taught in class.
Unfortunately, symbols, words and formulas vary, so I did not throw in any.
Besides, we need more reasoning/understanding, and less formula-memorizing.
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