The number of configurations W(N,z; r,v r ,α i ; M,β i ,x i ) of a polymer in a field of fixed obstacles is obtained. The cubic lattice of N sites has a coordination number z and is of d=z/2 dimensions. The obstacles are modeled as rigid rods or rigid but bent polymers of length r and of volume fraction v r . A fraction α i of the obstacle bonds are oriented in orientation i. The flexible polymer which we place into the field of rigid obstacles is of length M, has β i of its bonds lying in orientation i, and has an end to-end-length given by x i . The formula for W results in expectation values only a few percent different from the exact expressions for the known special cases