SOLUTION: ann, donna, fay, bob, and carl all want to go to the movies but ann and donna got into a fight and can not sit together in the movie theater. how many ways can they be seated in a

Question 915469: ann, donna, fay, bob, and carl all want to go to the movies but ann and donna got into a fight and can not sit together in the movie theater. how many ways can they be seated in a row?

Found 2 solutions by ewatrrr, josmiceli:
Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!
5 people
5! - 4! = 120 - 2*24 = 72 ways
4! being number of ways if they did sit together
(considering them as one Unit)
2*4! allowing for them to sit on either side of one another
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
This would be all the possible ways that
the 5 of them can sit together minus
the ways that Ann and Donna can be
seated together:
----------------
The ways 5 people can sit together is:

----------------
The ways Ann and donna can sit together is:
a d x x x
d a x x x
---------
x a d x x
x d a x x
---------
x x a d x
x x d a x
---------
x x x a d
x x x d a
---------
For each of these 8 cases, the x's
can have:
different orderings
-------------

and
There are 72 ways they can be seated in a row
Hope I got it

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