Why is it that there are sharper Maxima with higher number of slits in a grating

In the double slit experiment the photons that enter the slits all end up in the bright areas, there are no photons in the dark. Feynman proposed the photons "look" at all possible pathways and choose the ones that are most probable, the paths highly tend to be the ones that are of length that is an integer multiple of the wavelength, intuitively these photons travel in space from atom A to atom B like a musical note travels on a piano or guitar string. Also the photon tends to want to travel a shorter distance.

The "looking" process involves an excited electron causing disturbances in the EM field (called virtual photons), when there are many slits the EM field concentrates (resonates) in the middle, i.e. the other paths thru the slits are more difficult to traverse due to their tighter path lengths and become less probable.