SOLUTION: A class has 15 girls and 19 boys. A committee is formed with two girls and two boys, each with a distinct responsibility. Determine whether this situation involves a permutation or

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Question 875414: A class has 15 girls and 19 boys. A committee is formed with two girls and two boys, each with a distinct responsibility. Determine whether this situation involves a permutation or a combination. Then determine the number of possible arrangements.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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 = 71,820 ways to form this committee.