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A permutation of 5 digits from the set ...

A permutation of 5 digits from the set `{1,2,3,4,5}` where each digit is used exactly once, is chosen randomly. Let `p/q` expressed as rational in lowest form be the probability that the chosen permutation changes from increasing to decreasing, or decreasing to increasing at most once e.g. the strings like `12345,54321,12543 and 53214` are acceptable but strings like `13245 or 53241` are not.find `(p+q)`.

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