document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=997223>Question 997223</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many permutations can be made from the letters of the word \"WHITE\" with vowels and consonants alternating? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #615430 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=615430\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i believe it's going to be 2! * 3! = 2 * 6 = 12.\r<BR>\n" );
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document.write( "the consonants have to be on the outside and the vowels have to be on the inside.\r<BR>\n" );
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document.write( "why?\r<BR>\n" );
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document.write( "because if a voowel is on the outside than 2 consonants have to be together.\r<BR>\n" );
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document.write( "let c = consonant<BR>\n" );
document.write( "let v = vowel\r<BR>\n" );
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document.write( "cvcvc is ok<BR>\n" );
document.write( "vcvcc is not ok<BR>\n" );
document.write( "ccvcv is not ok.\r<BR>\n" );
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document.write( "so vowels have to be in the middle.\r<BR>\n" );
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document.write( "so slots 1, 3, and 5 have to be consonants.<BR>\n" );
document.write( "and slots 2 and 4 have to be vowels.\r<BR>\n" );
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document.write( "within the 3 consonent slots, you can lay the consonents out in 3! = 6 ways.\r<BR>\n" );
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document.write( "within the vowel slots, you can lay the vowels out in 2! = 2 ways.\r<BR>\n" );
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document.write( "the total number of ways is therefore 3! * 2! = 6 * 2 = 12 ways.\r<BR>\n" );
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document.write( "since the number of vowels and consants is small, we can actually lay them out so you can say how it works.\r<BR>\n" );
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document.write( "the consonents are wht<BR>\n" );
document.write( "the vowels are ie\r<BR>\n" );
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document.write( "the different number of ways the vowels can be layed out are:\r<BR>\n" );
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document.write( "ie<BR>\n" );
document.write( "ei\r<BR>\n" );
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document.write( "the different number of ways the consonents can be layed out are:\r<BR>\n" );
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document.write( "wht<BR>\n" );
document.write( "wth<BR>\n" );
document.write( "hwt<BR>\n" );
document.write( "htw<BR>\n" );
document.write( "twh<BR>\n" );
document.write( "thw\r<BR>\n" );
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document.write( "now, for wht, you can intersperse ie two different ways.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "wihet<BR>\n" );
document.write( "wehit\r<BR>\n" );
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document.write( "for wth, you can intersperse ie two different ways.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "witeh<BR>\n" );
document.write( "wetih\r<BR>\n" );
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document.write( "you can do the same for all 6 possible combinations of the consonents, so the total number of ways is 6 * 2 = 12.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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