Question 875414
Keyword to look out for: distinct


Since each person has a "distinct responsibility" this means order matters. If you were to alter the order, then the two people would have different responsibilities.


So we're using a permutation.


There are 15 P 2 = (15!)/(15-2)! = (15*14*13!)/(13!) = 15*14 = 210 different ways to pick 2 girls (order matters).



There are 19 P 2 = (19!)/(19-2)! = (19*18*17!)/(17!) = 19*18 = 342 different ways to pick 2 boys (order matters).



There are 210*342 = <font color="red">71,820</font> ways to form this committee.