George is planning a dinner party for three other couples, his wife, and himself. He plans to seat the four couples around a circular table for 8, and wants each husband to be seated opposite his wife. How many seating arrangements can he make, if rotations and reflections of each seating arrangement are not considered different? (Note: In this problem, if one seating is a reflection of another, then the two are considered the same!)
George can be anywhere in the 8 seats. Since rotations and reflections don't there' only one way for George and his wife to be seated. Then afer that next to them there are 3 choices for the husband/wife, and then the other partner is picked. Then after that, there are two choices, then 1. So the number of ways is 3*2*1 = 6.