Graph Algorithms · Superchallenge problem

A weighted graph has vertices $s,a,b,c,d,t$ and edges $sa{:}3, sb{:}3, ac{:}4, bc{:}4, at{:}10, ct{:}2, bd{:}6, dt{:}1$. Considering every shortest path from $s$ to $t$ (there may be more than one), how many of the graph's $8$ connections appear in AT LEAST ONE shortest path?