Arsene_Wenger 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?

I know sample space is 120 (5!) and hence the denominator. What do we manipulate to get the numerator, given the info. above?

Outcomes one couple is sitting together: 4!*2

Outcomes the other couple is sitting together: 4!*2

Outcomes that both couples are sitting together: 3!*2*2

Outcomes neither couples are sitting together

=5!-4!*2-4!*2+3!*2*2

=5!-(24-6)*4=120-72=48

Probability =48/120=2/5