Probability of a Permutation

I wanted to know how to compute for the probability of a certain string to appear in a permutation.

For example: What's the probability that when I flip a coin five times, two heads or two tails appear in a row?

I know that the probability is $\frac{15}{16}$ because $\text{THTHT}$ and $\text{HTHTH}$ are the only permutations not containing two faces in a row.

But I wanna know how to compute for the probability.

For example, what's the probability that when I flip a coin $20$ times, I get H then T then an H again in those flips?

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$