imc

First, choose the two letters to be repeated in each set. $\left(\genfrac{}{}{0ex}{}{5}{2}\right)=10$. Now we have three remaining elements that we wish to place into two separate subsets. There are $2^3=8$ ways to do so because each of the three remaining letters can be placed either into the first or second subset. Both of those subsets contain the two chosen elements, so their intersection is the two chosen elements). Unfortunately, we have over-counted (Take for example $S_1=\{a,b,c,d\}$ and $S_2=\{a,b,e\}$). Notice how $S_1$ and $S_2$ are interchangeable. Division by two will fix this problem. Thus we have: $\frac{10\times 8}{2}=40⟹\boxed{40}$