A group of people sit around a table. There are 4 couples and 2 singles... What is the probability that everyones request will be met?

Question

A group of people sit around a table. There are 4 couples and 2 singles. The couples want to sit together and the singles have asked to be seated apart. the seating is randomly chosen what is the probability that everyones request will be met?

Answer 1

Where you start doesn't matter: you can pick the first single in 2 ways,

the the couples can be seated in 8*6*4*2 ways and the remaining single person can then be placed in any one of the 3 places between the couples.

2*8*6*4*2*3/9! should be the probability = 1/1260

I think this is correct, but I am not absolutely certain. If you get another & better answer, I would like to know about it. Thank you.