SOLUTION: Consider the word “DIGITALCIRCUITS”. How many arrangements are possible such that vowels and consonants occur in alphabetical order independently ? (Example: For the word “APPLE th

Algebra ->  Algebra  -> Permutations -> SOLUTION: Consider the word “DIGITALCIRCUITS”. How many arrangements are possible such that vowels and consonants occur in alphabetical order independently ? (Example: For the word “APPLE th      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 495196: Consider the word “DIGITALCIRCUITS”. How many arrangements are possible such that vowels and consonants occur in alphabetical order independently ? (Example: For the word “APPLE these are some of the possibilities “ALEPP” “ALPEP” and “LAPEP”)

Answer by richard1234(5390) About Me  (Show Source):
You can put this solution on YOUR website!
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.