Specific coin order given three heads in five

Question

Five fair coins are tossed in sequence. You learn that exactly three of them landed heads. What is the probability that the order of results was $T,H,H,T,H$ ?

Short answer

$1/10$ . Conditioning on exactly three heads leaves $\binom53=10$ equally likely arrangements, and $THHTH$ is one of them.

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Lessons behind this question

Sample Spaces, Events, and the Probability Axioms
Conditional Probability, Total Probability, and Bayes' Rule
Worked Examples — Probability Trees, Monty Hall, and Bayesian Updating

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