Application of HCR's Formula on Circular Permutations

Algebra Level pending

All the clock-wise circular permutations, obtained by permuting the letters A, B, B, B, C, C, C, D, E, F, G, H together, are arranged in the correct alphabetic order. Find out the alphabetic order of a randomly selected clock-wise circular permutation (as shown in the figure above)


The answer is 1105185.

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