Counting The Sixes

Probability Level 3

A fair, 66-sided die is rolled 2020 times, and the sequence of the rolls is recorded.

CC is the number of times in the 20-number sequence that a subsequence (of any length from one to six) of rolls adds up to 6.6. These subsequences don't have to be separate and can overlap each other. For example, the sequence of 2020 rolls 12334222111366141523 12334222111366141523 contains the ten subsequences 123,33,42,222,2211,1113,6,6,141,15123, 33, 42, 222, 2211, 1113, 6, 6, 141, 15 which all add up to 6,6, so C=10C=10 in this case.

The expected value of CC is equal to ab\frac{a}{b} for coprime positive integers aa and b.b.

What is a+b?a+b?


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