SOLUTION: A family of 6 boys and 3 girls. Mother wanted to choose 4 of them to prepare dinner: What is the probability of choosing a boy to prepare tea, a boy to cook, and two girls to proc

The total number of ways to assign jobs    is

     = 9*8*21 = 1512.


(9 ways to fill the first position; 8 ways to fill the second position;
and  ways to fill the 3-rd and 4-th positions with possible transposition there).


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    |   Now let's calculate the number of ways  |
    |      to assign jobs as described.         |
    +-------------------------------------------+


The number of ways to select one boy from 6 boys to prepare tea is 6.            

The number of ways to select 1 boy from remaining 5 boys to cook is 5.

The number of ways to select 2 girls from 3 girls is 3.


So, the number of ways to form a proper team as described is 6*5*3 = 90.


The probability under the problem's question is

          number of proper ways       90     5
    P = ------------------------- = ----- = ---- = 0.05952  (rounded).    ANSWER
          total number of ways       1512    84



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    |   Another way  to solve is to write   |
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    P =  =  =   (the same answer).


Here    is the probability to select one of 6 boys from 9 kids to prepare tea.

        is the probability to select one of remaining 5 boys from remaining 8 kids to cook.

        is the probability to select two of 3 girls from remaining 7 kids to process table.