Five married couples are randomly paired at a rectangular table. Five wives on one side and five husbands on the other side. What is the probability that only one man soy across from his wife.
Here's what I got. I assume A-1 B-2 C-3 D-4 and E-5 are couples. Where letters are wives and numbers are husband.
Suppose a-1 sit across. Then b only has 3 choices because she can't sit across her husband. So as c, who only has 3 choices. Then d has 2 choices and e had the pair up with whatever's left. So the probavility I got is (5* 3*3*2*1 ) / 5!
Am I right?