A new selection rule for transmission under small voltage for molecular electronic devices consisting of alternant hydrocarbons is established, based on curly arrow draw- ings of the displacement of electrons through the conjugated system of the molecule. If the displacement of electrons from one contact atom to the other can be drawn, trans- mission is possible. If not, then no transmission will take place. This simple, back of the envelope ansatz allows determination of quantum interferences for a wide range of exper- imentally studied molecules (linear polyenes, benzenoids, cross-conjugated molecules,...) avoiding any calculation. This new selection rule bridges the conceptual gap between traditional reactivity theory and molecular electronics.