We are counting photons in this experiment, so we can use
Poisson statistics.  The noise is the square root of the signal
plus the background.  Thus,

 (a) S/N = 500 / sqrt(500) = 22
 (b) S/N = 500 / sqrt(500+500) = 16
 (c) S/N = 500 / sqrt(500+5000) = 6.7