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

Algebra ->  Permutations -> 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       Log On


   

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) About Me  (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) About Me  (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:
+5%2A4%2A3%2A2%2A1+=+120+
----------------
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:
+3%2A2%2A1+=+6+ different orderings
-------------
+6%2A8+=+48+
and +120+-+48+=+72+
There are 72 ways they can be seated in a row
Hope I got it