Answer to Question #338223 in Statistics and Probability for Flora

Question #338223

How many different samples of size 8 can be selected from a population with a size of 12 ?




1
Expert's answer
2022-05-09T09:42:13-0400

Consider two cases: samples without replacement (the order of elements in samples does not matter) and samples with replacement (the order of elements in the sample matters). In the first case we receive C128=12!8!4!=91011124!=9511=495C_{12}^8=\frac{12!}{8!4!}=\frac{9\cdot10\cdot11\cdot12}{4!}={9\cdot5\cdot11}=495 . The number of different samples is equal to the number of subsets of size 88 of the set of size 1212. The number of samples with replacement (the order of elements matters) is equal to 12812^8. We used the multiplication principle of combinatorics.

Answer: there are 495495 samples without replacement(the order of elements does not matter) and 12812^8 samples with replacement(the order of elements matters).


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