We know from Section 2.3 that there are

possible SRS€™s of size n from a population of size N. Suppose we stratify the population into H strata, where each stratum contains Nh = N/H units. A stratified sample is to be selected using proportional allocation, so that nh = n/H.
a. How many possible stratified samples are there?
b. Stirling€™s formula approximates k!, when k is large, by

Where,

Use Stirling€™s formula to approximate

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e = exp (1 ) ~ 2.718282. number of possible stratified samples of size n number of possible SRSs of size n