Probability, random line up Five distinct families arrive to a party. Each family consists of 3 people. The 15 participants of the party are arranged randomly in a line. 
Let X be the number of families that their members sit next to each other. Find E[X] and Var(x).

My attempt: Just go straight to find out the pmf of X, P(X=1), P(X=2)... up to P(x=5). Does this question ask for all members of at least 2 of the family members? If it is the second case, I have no idea how to do it. 

Hint: The random variable takes values $0,1,2, \cdots 5$. Find the probability of each event. Also, $X^2$ takes values $0,1,4,16,25$ with the same probabilities, as computed above, and $Var(X)=E(X^2)-E(X)^2$
