Motivated by physics, we define the scattering equations and count the number of solutions separated by irreducible components of the scattering correspondence. We then define a subvariety V(k,n) of the Grassmannian Gr(k,n) and show that the coefficient in front of a special Schubert class in the fundamental class of V(k,n) counts the solutions to scattering correspondence component by component. Finally, we study V(3,n), giving its fundamental class and its ideal in Plücker coordinates.