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How many ways can Amir, Bin, Charles, and Daria stand in a line if Amir and Bin refuse to stand next to each other?

 May 22, 2021
 #1
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Let's  suppose   that  we  can let anyone  stand  anywhere.....there  are 4!  = 24  ways to do this

 

If Ben  and Amir DO  stand next to each other  they can occupy  any 3 postions  and be  arranged in 2  ways  for  each of  these   =    3 * 2  =  6 ways

 

So....the  number of ways  they can  be arranged  where  they ARE NOT standing next to each other  =

 

24  -  6    =    18  ways

 

cool cool cool

 May 22, 2021

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