Baldness is A Solution

[S2 Maths and Up: Probability]

How likely is it for two people to have the same number of hairs on their head?

Just asking for the head only, let's save the total amount of hair on the body for another day. Some people have hairy arms, some have two strands growing from a single follicle, there's enough confusion as is.

Fermi estimates are a fairly powerful tool to use as a way to establish a hypothesis. Whether it's proven or disproven is another matter altogether, and as shown, it is prone to being disproved.

The pigeonhole principle, however, is a certified measure to analyse such means. You may find it useful in a future question, keep your eyes peeled!