preyshi wrote:

Two couples and one single person are seated at random in a row of five chairs. What is the probability that neither of the couples sits together in adjacent chairs?

total # of ways of seating two couples and one single person = 5! =120

total # of ways both couples can sit together = 3!*2!*2!= 24 ways

total # of ways ONLY one couple can sit = 4! * 2!

- 3! *2*2 = 24

(Subtract the # of ways where we have both couples sitting together)

favorable ways = 120- 24 -24 = 72 ways

total ways = 120

probability = 72/120 = 3/5