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Two girls and three boys sat in a five-seat row at the movie theater. What is the probability that the two people on the ends of the row were both boys or both girls?
 Aug 8, 2016
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+5

The total arrangements possible = 5!  = 120

 

If the two girls sit at both ends, we can seat the girls in two ways and everyone else in the middle 3! = 6 ways. So, the number of possible arrangements =  2 * 3!  =  12

 

And we can choose any 2 of the 3 boys to sit at both ends and we can arrange them in two ways. And for each of these arrangements, everyone else in the middle can be arranged in 3!  = 6 ways. So the number of possible arrangements =  C(3,2) *2 * 3! *   = 36

 

So........the probability that a girll sits at both ends or a boy sits at both ends = [ 12 + 36] / 120  = 48/120   = 2.5  = 0.40

 

 

cool cool cool

 Aug 8, 2016

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