There are times the independence criteria might not be satisfied, but for all practical purposes the binomial distribution could still be used. The question is whether the total population is large enough relative to the number of samples. If the population size is at least 20 times larger than the sample size then it could be considered a binomial event. (Some textbooks use 10 instead of 20, and 10 is also a valid criterion. The important thing is that you use a widely accepted standard when justifying that your situation can be considered binomial