Here is what i thought.
(4P2 x 5P5) + ( 3P2 X 5P5 ) = 2160
Hope it helps.
Q: A rectangular table has 7 secured seats, 4 being on one side facing the window and 3 being on the opposite side. In how many ways can 7 people be seated at the table if 2 people, X and Y must sit on the same side?
The answer I was given is 2160, but I don't know how to derive it...>.< Thank you for helping!
Hello, Tangera!
A rectangular table has 7 secured seats, 4 on one side, 3 on the other. In how many
ways can they be seated at the table if 2 people, and must sit on the same side?
Suppose and sit on the 4-side of the table.
. . X has 4 choices of seats; Y has 3 choices of seats.
. . The other five can be seated in ways.
There are: . ways.
Suppose and sit on the 3-side of the table.
. . X has 3 choices of seats; Y has 2 choices of seats.
. . The other five can be seated in ways.
There are: . ways.
Therefore, there are: . seating arrangements.