6 friends went to the cinema to watch a new movie. Then they realized that 2 of them are a couple and cannot be separated. How many different ways they can sit in the movie theatre?
I'm assuming they sit in a group ... not scattered throughout the theatre. Here's what I get:
They'll sit in 6 seats in a row. Call the couple XX and the others A, B, C, D.
The first way is the couple first: X X A B C D
then X X A B D C
X X A C B D
X X A C D B
and so on. There are 24 of these.
Move the couple over to the 2nd and 3rh seats: A X X B C D
A X X B D C
same permutations as above. There are 24 of these.
There are 5 positions where X X can sit. Each of these 5 positions can seat the other 4 friends 24 ways.
So, 5 x 24 = 120 ways to seat the people.
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