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Answer to Question #11002 in Statistics and Probability for Ke_091

Question #11002
A committee of four is to be formed from among 5 economists, 6 engineers, 3 statisticians and 1 doctor . Find the probabilities that,
(i) Each profession is represented in the committee
(ii) It has a doctor and at least one economist
(iii) It has a doctor and at least one economist and others from remaining members
Expert's answer
A committee of four is to be formed from among 5 economists, 6 engineers, 3 statisticians and 1 doctor. Find the probabilities that,
(i) Each profession is represented in the committee

The total number of possible committees is С(5+6+3+1,4).

P = (С(5,1)+С(6,1)+С(3,1)+С(1,1))/С(5+6+3+1,4) = (5+6+3+1)/С(15,4) = 15/1365 ≈ 0.0110.

(ii) It has a doctor and at least one economist

There is C(5,1) = 5 ways to choose one economist and С(15-1-1,2) ways to choose others (excepting one economist and a doctor). So,

P = (С(5,1)+С(15-1-1,2))/С(5+6+3+1,4) = (5+C(13,2))/1365 = (5+78)/1365 ≈ 0.0608.

(iii) It has a doctor and at least one economist and others from remaining members

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