Answer to Question #264118 in Statistics and Probability for Nathan

Question #264118

The director of a small management consulting company is to form a team of 5 management consultants from the 12 available to run a workshop. Exactly 8 of the 12 have sound presentation skills. Two of the 8 with sound presentation skills are feuding and cannot both be on the same team. In how many ways can a team of 5 management consultants that includes 3 with sound presentation skills be selected?

1
Expert's answer
2021-11-15T18:38:56-0500

In how many ways can 3 management consultants having  sound presentation skills be selected?


"\\dbinom{8}{3}=\\dfrac{8!}{3!(8-3)!}=\\dfrac{8(7)(6)}{1(2)(3)}=56"

Two of the 8 with sound presentation skills are feuding and cannot both be on the same team.  Then In how many ways can 3 management consultants having  sound presentation skills be selected now?

"\\dbinom{8}{3}-(8-2)=50"

In how many ways can 2 management consultants without  sound presentation skills be selected?


"\\dbinom{12-8}{5-3}=\\dfrac{4!}{2!(4-2)!}=\\dfrac{4(3)}{1(2)}=6"

In how many ways can a team of 5 management consultants that includes 3 with sound presentation skills be selected now?


"50(6)=300"


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