Tyi000111 wrote:
Six people are to be seated at a round table with seats arranged at equal distances. Andy and Bob don’t want to sit directly opposite to each other. How many seating arrangements are possible?
The approach explained in
Veritas Prep goes like this
- Andy takes one seat out of the 6 in the circular arrangement
- Bod has 4 options options excluding the one in front of Andy
- Remaining 4 people can sit in 4! ways
- Total Arrangements: 1*4*4!
I was trying to test the following approach but wasn't able to get the right answer
- Total arrangements without constraints = 5!
- Ways in which Andy and Bod sit opposite to each other = 2 (they both can switch seats)
- Remaining 4 people can sit in 4! ways
- Total arrangements considering constraints = 5! - 2*4! = 72
I don't understand what error I am making here and would appreciate the help