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In how many ways can 8 people be seated in a row of chairs if three of the people, John, Wilma and Paul, refuse to sit in three consecutive seats?

mathtoo  Aug 25, 2018
 #1
avatar+91027 
+2

The total arrangements possible  = 8!

 

Now...let's consider the arrangements possible if all three DO sit together [in consecutive seats ]

 

Considering them as  a single entity....they can be arranged  as 3!  = 6 ways

 

And they can be seated in any 6 positions  [ positions 1 - 6 ]  = 6 ways

 

And for each of these arrangements the other people can be seated in 5!  = 120 ways

 

So...the total arrangements possible if they DON'T sit together   =

 

Possible arrangements  - Arrangements where they sit together  =

 

8!  - [ 6 * 6 * 5!]  =

 

40320 - 36*120  =

 

40320   - 4320  =

 

36000  ways

 

 

cool cool cool

CPhill  Aug 25, 2018

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