We consider the symmetric exclusion process {\\eta_t,t>0} on {0,1}^{Z^d}. We fix a pattern A:={\\eta:\\sum_{\\Lambda}\\eta(i)\\ge k}, where \\Lambda is a finite subset of Z^d and k is an integer, and we consider the problem of establishing sharp estimates for \\tau, the hitting time of A. We present a novel argument based on monotonicity which helps in some cases to obtain sharp tail asymptotics for \\tau in a simple way. Also, we characterize the trajectories {\\eta_s,s\\le t} conditioned on {\\tau>t}.