Simple random sampling, or random sampling without replacement, is a sampling design in which is distinct units are selected from the N units in the population in such a way that every possible combination of n units is equally likely to be the sample selected. The sample may be obtained through is selections in which at each step every unit of the population not already selected has an equal chance of selection.
Equivalently, one may make a sequence of independent selections from the whole population, each unit having an equal probability of selection at each step, discarding repeat selections and continuing until n distinct units are obtained.
A simple random sample of n = 40 units from a population of N = 400 units is depicted in Figure below:
Designs other than simple random sampling may give each unit equal probability of being included in the sample. but only with simple random sampling does each possible sample of is units have the same probability.