An Unlucky Situation

There is an unbiased cubical die with its faces labeled as \(A, B, C, D, E \) and \(F\). If the die is thrown \(13\) times, what is the probability that no two consecutive throws show up consonants?

The answer is of the form \[\dfrac{a \times b }{c^{d}}\]

where \(a,b,c\) are co-prime while \(c,d\) are not .

Find \(a\times b\times c\times d\) .

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This question is a question that I had got wrong in my Coaching Class's Test\[\]
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