Probability Mania

A fair six-faced die is rolled six times.
The probability that the numbers on the die appear either in ascending or descending order is of the form \[\dfrac{A}{B}\] where \(A\) and \(B\) are co-prime integers.
Find the value of \[\dfrac{B}{24}-A\]

- The order may not be strictly ascending or descending. For example, \(1-1-2-4-4-6\) is a valid sequence of numbers.


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