Math Problem (why can't I...)?

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Incis0r

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Math Destroyer 2013
Test 1, # 38

Five chairs are lined up in a row. How many ways can three boys and two girls sit in these chairs if the girls always sit side by side?

I understand that it is 4 x 2(possible side by side configurations of girls) x 3! (Possible configurations of guys) = 48.

What I am wondering, however, is why can't I use permutations and combinations?


For example, why can't i do 5P2 (for the girls) * 3! (For the guys). That answer gives me 60.

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Math Destroyer 2013
Test 1, # 38

Five chairs are lined up in a row. How many ways can three boys and two girls sit in these chairs if the girls always sit side by side?

I understand that it is 4 x 2(possible side by side configurations of girls) x 3! (Possible configurations of guys) = 48.

What I am wondering, however, is why can't I use permutations and combinations?


For example, why can't i do 5P2 (for the girls) * 3! (For the guys). That answer gives me 60.

5P2 means how many ways you can select 2 things out of 5 where order matters. The question is asking for how many ways you can arrange 5 things in a row in which 2 things have to be next to each other.
For these type of problems, pay a close attention to the way the question is worded.
 
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