The binomial distribution is a discrete probability distribution. It shows the probability of getting 'd' successes in a sample of 'n' taken from an 'infinite' population where the probability of a success is 'p'.
(note the similarity to the normal distribution)
The binomial distribution would be appropriate if items taken from a process were inspected. If the proportion of defective items is 'p' then the binomial distribution gives the probability of finding 'd' defectives in a sample of 'n':
A distribution that describes the probability distribution for discrete (attribute) variables.
Hypergeometric Distribution 

The Hypergeometric distribution is used when a fairly small sample is taken from a reasonably small population without replacement. This is the method most often used in sampling inspection.
The equation is cumbersome; for reasonably large samples both the numerator and denominator become so large that even computers have problems dealing with them; even though the answer is small.
The Poisson distribution is a discrete distribution used when the sample is unbounded. It is often used to find the probability of a given number of events in a given time.
The symbol 'l' represents the average number of occurrences.
This is often used in reliability engineering in the form:
This is the probability of zero faults, or the probability of the device not failing, in time 't'. Note that definition of 'l' has changed to the average number of occurrences per unit time. Hence 'lt' is the average number of the faults in the time period of interest.
