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The vowels and consonants, respectively, are AIIIIU and CCDGLRSTT. Assuming two of the same letter are indistinguishable, there are
ways to arrange the letters.
Consider only the vowels. Out of the 6!/4! = 30 distinguishable ways to arrange them, only one is in alphabetical order. For the consonants, out of the 9!/2!2! = 90720 ways to arrange, only one is in alphabetical order, so we divide N by 30 and then by 90720, leaving 5005 ways.