The total number of ways to assign jobs    is

     = 10*9*28 = 2520.


(10 ways to fill the first position; 9 ways to fill the second position;
and  = 28 ways to fill the 3-rd and 4-th positions with possible transposition there).


    +-------------------------------------------+
    |   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 4 girls is   =  = 6.


So, the number of ways to form a proper team as described is 6*5*6 = 180.


The probability under the problem's question is

          number of proper ways      180     1
    P = ------------------------- = ----- = ---- = 0.07143  (rounded).    ANSWER
          total number of ways       2520    14



    +---------------------------------------+
    |   Another way  to solve is to write   |
    +---------------------------------------+


    P =  =  =   (the same answer).


Here    is the probability to select one of 6 boys from 10 kids to prepare tea.

        is the probability to select one of remaining 5 boys from remaining 9 kids to cook.

       =   is the probability to select one of 6 possible pairs (girl,girl) 
                                                         from 28 possible pairs (kid,kid) to process table.