Eight people are put into pairs and enter a room with a large table with four pairs of chairs (2 chairs and a lot of space then 2 more chairs and a lot of space and so on) Though they could sit anywhere they had to sit with there assigned partner. In How Many ways could the eight people have sat around the table ensuring that each pre-assigned pair was sitting at a pre-set pair of the chairs

Question

Eight people are put into pairs and enter a room  with a large table with four pairs of chairs (2 chairs and a lot of space then 2 more chairs and a lot of space and so on) Though they could sit anywhere they had to sit with there assigned partner. In How Many ways could the eight people have sat around the table ensuring that each pre-assigned pair was sitting at a pre-set pair of the chairs

drwls · Answer

The first assigned pair has four pairs of chairs to choose from. The second has three and the third has two. In each case, the pair can do a left-right switch. That makes 4x3x2x2 = 48 possibilities.