+0  
 
+2
129
1
avatar+262 

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?

Darkside  Sep 3, 2018
 #1
avatar+2778 
0

I think it's easiest to count the ways that they can consecutively sit together and subtract this from the total number of seating arrangements.

 

There are 6 groups of 3 consecutive seats.  Within each group there are 3!=6 ways the three fussy people can be arranged.

 

Then the remaining 5 people can be arranged 5!=120 ways in the remaining seats.

 

So there are 6*6*120 = 4320 arrangements where they DO sit consecutively

 

There are 8! = 40320 total arrangements.

 

So there are 40320 - 4320 = 36000 arrangements where the 3 do not sit consecutively.

Rom  Sep 5, 2018

19 Online Users

avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.