Binomial - Random variable #X# is the number of successes in n independent and identical trials, where each trial has fixed probability of success.
Hypergeometric - Random variable #X# is the number of objects that are special, among randomly selected #n# objects from a bag that contains a total of #N# out of which #K# are special. If #n# is much smaller than #N# then this can be approximated by binomial.
Poisson - Random variable #X# counts the number of occurrences on an event in a given period, where we know that the concurrences has an average of #\lambda# for any period of that length, independent of any other disjoint period.