Question 1148152
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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  {{{7/16}}};

     The probability to select a teacher at the 2-nd selection is  {{{6/15}}};

     The probability to select a teacher at the 3-rd selection is  {{{5/14}}}.


     Therefore, the answer to (a) is  the product  {{{7/16}}}.{{{6/15}}}.{{{5/14}}}.


     You compute it.



(b)  By analogy, 


          The probability to select no teacher at the 1-st selection is  {{{9/16}}},    (where 9 = 3 + 6)

          The probability to select no teacher at the 2-nd selection is  {{{8/15}}};

          The probability to select no teacher at the 3-rd selection is  {{{7/14}}}.


     Again, you compute it.
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Solved, answered, explained and completed.