If we treat S as the sum of two Bernoulli random variables Xi and Yi, where Xi and Yi indicate whether the first person and second person in the couple are still alive. I'm stuck here.
This is a conditional expectation. You want to find $\displaystyle E[S|A=a] $. This is saying that you want to find the expected number of couples with both partners alive given that $\displaystyle a $ people are alive. So this expectation depends on $\displaystyle a $ (e.g. a function of $\displaystyle a $).