The Pigeonhole Principle and the Law of Large Numbers are related but they are not the same thing.

The Pigeonhole Principle is a mathematical principle that states that if you have more items than containers, and you distribute the items randomly into the containers, at least one container must contain more than one item.

The Law of Large Numbers is a statistical theorem that describes the behavior of the average of a large number of independent, identically distributed random variables. The theorem states that as the number of observations increases, the average of the observed values converges to the expected value.

In the case of the number of hairs on a human body, the Pigeonhole Principle suggests that since there are more people on earth than there are possible numbers of hairs on a human body, it is likely that at least two people have the same number of hairs. The Law of Large Numbers, on the other hand, is not directly relevant to this question, since it concerns the behavior of averages of large numbers of random variables, rather than the distribution of a single variable among a large population.
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