It is sometimes important to know how many paths there are between to vertices in a directed graph (for instance, to calculate the resilience to failures in a network). Let #PATH = { (G,s,t,k) | There are exactly k simple paths from s to t in the directed graph G}. Prove that #PATH E PSPACE. It is sometimes important to know how many paths there are between to vertices in a directed graph (for instance, to calculate the resilience to failures in a network). Let #PATH = { (G,s,t,k) | There are exactly k simple paths from s to t in the directed graph G}. Prove that #PATH E PSPACE