Randomising twenty people

Topic: Studies, data, and evidence · more questions on this topic
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Twenty people are split at random into a test group and a control group of ten. How many different test groups are possible?

Worked answer (click to show)

A test group is an unordered choice of 10 people from 20, so there are

\binom{20}{10}=\frac{20!}{10!\,10!}=184\,756

possible test groups. Randomisation picks one of them with equal probability, for example with sample(1:20, 10).