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Find the number of distinct permutations of the string AAABBBBCCDDDEEFFGGHHIIJ which contain substrings BEEF, HIGH and...

Find the number of distinct permutations of the string AAABBBBCCDDDEEFFGGHHIIJ which contain substrings BEEF, HIGH and DIG and in which all letters A, B and D and G appear in that order (that is, all As appear before all Bs, all Bs appear before all Ds and all Ds appear before all Gs), but not necessarily next to each other.

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