document.write( "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”)
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Algebra.Com's Answer #336009 by richard1234(7193) $\"\"$ $\"About$

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The vowels and consonants, respectively, are AIIIIU and CCDGLRSTT. Assuming two of the same letter are indistinguishable, there are\r
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ways to arrange the letters.\r
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\n" ); document.write( "\n" ); document.write( "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. \n" ); document.write( "

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