Enumerative geometry of divisorial families of rational curves

We compute the number of irreducible rational curves of given degree with I tacnode in P-2 or I node in P-3 meeting an appropriate generic collection of points and lines. As a byproduct, we also compute the Dumber of rational plane curves of degree d passing through 3d - 2 given points and tangent to a given line. The method is 'classical', free of Quantum Cohomology.