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In how many different ways can four students stand in a straight line if two of the students refuse to stand next to each other?

 Dec 19, 2019
 #1
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There are 8 ways.

 Dec 19, 2019
 #2
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I will assume the students are distinguishable and 'a' and 'b' will not stand next to each other...

 

a - - b

b - - a

a - b -

b - a  -

- a - b

- b - a         are six ways for  a  and b  NOT to be next to each other. 

    There are tow ways EACH for  c   and  d to fill in the blanks for each of these six ways

         6 x 2 = 12 ways

 Dec 19, 2019

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