Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
# of ways both couples can sit together:
2 ways to pick 2 couples
4 ways they can be seated so that the couples are adjacent.
3! ways to seat the 2 couples with the single person
so total = 2.4.3! = 48
# of ways 1 couple can sit together
2 ways to pick 1 couple from 2
2 ways they can be seated adjacent to each other
now this couple need to be seated with 3 other individuals with the constraint that the other couple cannot sit together, which is similar to seating 4C2 seating.
so total = 2.2.4C2 = 24
Total number of ways couple can sit together = 72
Problem is asking for Pb(not sitting together) = 5! - 72/5! = 48/120 = 2/5.