The discrimination between primary electrons and gamma rays is an open question for Imaging Atmospheric Cherenkov Telescops (IACTs) even in the Cherenkov Telescope Array (CTA) era. If the discrimination will be realized in the energy band around a few hundred GeV, the sensitivity for the observation of very-high-energy gamma rays will be improved by about an order of magnitude than that achieved by the CTA. Though the discrimination was tried by existing IACTs, the definitive methods have not been found yet. To figure out the problem, we have started basic simulations assuming an ideal detector that obtains the information on both the incident positions and directions for each Cherenkov photon. From the study, we recognized first that it is possible to discriminate only the Cherenkov photons generated around the point where incident particles first interact with the atmosphere, if the shower axis can be determined at accuracy. If the incident particle is an electron or positron, such Cherenkov photons are called the direct Cherenkov photons. On the other hand, if the primary is a gamma ray, they are the Cherenkov photons produced by the first electron-positron pair in an extensive air shower. We collectively call them the "first Cherenkov photons". Second we recognized that the ground pattern of the "first Cherenkov photons" for the electron is different from that for the gamma ray, which makes discrimination between these particles possible.