A permutation of 5 digits from the set \( \{1,2,3,4,5\} \) where each digit is used exactly once...

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A permutation of 5 digits from the set \( \{1,2,3,4,5\} \) where each digit is used exactly once, is chosen randomly. Let \( \frac{p}{q} \) expressed as rational in lowest form be the probability that the chosen permutation
\( \mathrm{P} \)
W. changes from increasing to decreasing, or decreasing to increasing at most once e.g. the strings like 1 \( 2345,54321,12543 \) and 53214 are acceptable but strings like 13245 or 53241 are not, find \( (p+q) \)
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