SOLUTION: A committee of three people is selected at random from a set consisting of seven ​teachers, three parents of​ students, and six alumni. a. What is the probability of the eve

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Question 1148152: A committee of three people is selected at random from a set consisting of seven ​teachers, three parents of​ students, and six alumni.
a. What is the probability of the event that the committee consists of all​ teachers?
b. What is the probability of the event that the committee has no​ teachers?
Answer by ikleyn(52798) About Me  (Show Source):
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(a)  The total set has 7+3+6 = 16 persons.


     The probability to select a teacher at the 1-st selection is  7%2F16;

     The probability to select a teacher at the 2-nd selection is  6%2F15;

     The probability to select a teacher at the 3-rd selection is  5%2F14.


     Therefore, the answer to (a) is  the product  7%2F16.6%2F15.5%2F14.


     You compute it.



(b)  By analogy, 


          The probability to select no teacher at the 1-st selection is  9%2F16,    (where 9 = 3 + 6)

          The probability to select no teacher at the 2-nd selection is  8%2F15;

          The probability to select no teacher at the 3-rd selection is  7%2F14.


     Again, you compute it.

Solved, answered, explained and completed.