Answer to Question #168368 in Statistics and Probability for Thomas

Question #168368

If exactly 4 boys volunteer, what is the probability that the team is all boys or no boys?


1
Expert's answer
2021-03-04T14:57:01-0500

There is not enough information to make conclusions. We assume in addition that there are 4 boys, m girls and the aim is to make a team with n persons, nm+4n\leq m+4 . In case we want to make a team from 4 boys, the total number of choices is: Cn4m=(n4)!m!(n4m)!C_{n-4}^{m}=\frac{(n-4)!}{m!(n-4-m)!} . I.e., we take 4 boys and for the other places take m girls. In case we wish to make a team with no boys, the number of choices is: Cnm=n!(nm)!m!C_n^m=\frac{n!}{(n-m)!m!}.


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