document.write( "Question 1191564: How many ways can you arrange the letters of the word EDUCATION, such that the vowels are always together?
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Algebra.Com's Answer #823364 by math_tutor2020(3817)\"\" \"About 
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\n" ); document.write( "The vowels in the order presented are: E, U, A, I, O
\n" ); document.write( "or perhaps better sorted as: A, E, I, O, U\r
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\n" ); document.write( "\n" ); document.write( "Think of the vowels as one block, and have some other letter (say X) representing that block.\r
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\n" ); document.write( "\n" ); document.write( "We go from the word EDUCATION to X,D,C,T,N
\n" ); document.write( "The initial 9 letter word drops to 9-5 = 4 letters after we kick out the vowels.
\n" ); document.write( "Then introducing letter X brings the count up to 5 letters.
\n" ); document.write( "Anywhere you see an X, replace it with some permutation of A,E,I,O,U.\r
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\n" ); document.write( "\n" ); document.write( "There are 5! = 5*4*3*2*1 = 120 ways to arrange X,D,C,T,N
\n" ); document.write( "And there are 5! = 120 ways to arrange the five vowels.\r
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\n" ); document.write( "\n" ); document.write( "Overall, there are (5!)*(5!) = 120*120 = 14400 different arrangements such that the vowels stick together.\r
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\n" ); document.write( "\n" ); document.write( "Answer: 14400
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