A specific sequence given three heads

EasyProbability Conditional Probability & Expectation~3m

Five fair coins are flipped. Given that exactly $3$ came up heads, what is the probability that the outcome was the specific sequence $T\,H\,H\,T\,H$ ?

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Given exactly $3$ heads, the $\binom{5}{3}$ head-placements are equally likely.
The target sequence is one of them: $1/\binom{5}{3}=1/10$ .

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A specific sequence given three heads

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