document.write( "Question 1112310: How do you do questions involving permuations where two things are arranged in alternative positions.
\n" ); document.write( "e.g.) How many ways can you arrange the letters in the word TRADE if the vowels and consonants have to be in alternative positions? \n" ); document.write( "

Algebra.Com's Answer #727362 by KMST(5328) $\"\"$ $\"About$

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The number of items in the two categories of items to be alternated
\n" ); document.write( "have to be the same of differ by 1.
\n" ); document.write( "As TRADE has 2 vowels, 3 consonants,, the arrangements would have to start and end with a consonant.
\n" ); document.write( "You have 3 consonants to arrange and $\"3%21=3%2A2=6\"$ ways to arrange them.
\n" ); document.write( "You have

choices for the order of the vowels.
\n" ); document.write( "You can make $\"6%2A2=12\"$ arrangements where you use all 5 letters in TRADE,
\n" ); document.write( "while alternating vowels and consonants.
\n" ); document.write( "If you try to do the same with the word TIRADE, you would have
\n" ); document.write( " $\"6\"$ choices for thew order of the vowels,
\n" ); document.write( " $\"6\"$ choices for thew order of the vowels,
\n" ); document.write( "and $\"2\"$ choices for what kind of letter to start with,
\n" ); document.write( "for $\"2%2A6%2A6=72\"$ arrangements made with all the letters in TIRADE,
\n" ); document.write( "alternating vowels and consonants. \n" ); document.write( "

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