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Two brothers and three sisters form a single line for a photograph. The two boys refuse to stand next to each other. How many different line-ups are possible?

 Nov 21, 2019
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Let the positions be   A  B   C   D     E     from left to right

 

There  are    C(5,2)  = 10 possible positions that the  boys can occupy

 

But  only 4 of them are together

AB  BC  CD   DE

 

So....6 of them aren't

And for each of these, the boys can be arranged 2 ways

And for each arrangement of the boys, the girls can be arranged in 3!  =  6 ways

 

So......the number of possible line-ups  =

 

6 * 2 * 6   =     72 possible line-ups

 

 

cool cool cool

 Nov 21, 2019

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