Use the inclusion-exclusion principle: Consider the set of 21 consonants and 5 vowels. How many distinct arrangement of 8 letters are there such that each letter appears exactly twice and no two...

Use the inclusion-exclusion principle:

Consider the set of 21 consonants and 5 vowels.  How many distinct arrangement of 8 letters are there such that each letter appears exactly twice and no two consecutive letters are the same.  For example, gghhmmww or kbbdkddee are not ok, but acacdgdg is.