document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=321453>Question 321453</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how many three digit numbers have only even digits?\r<BR>\n" );
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document.write( "How many ways are there to rearrange the letters in the word aptitude,if the first and last letter must each be a vowel? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #230237 by </B><A HREF=/tutors/aboutme.mpl?userid=galactus><B>galactus(183)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=galactus><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=galactus><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=230237\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are 4 even digits: 2,4,6,8\r<BR>\n" );
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document.write( "There are 4 choices for the first place, the second place, and the third place\r<BR>\n" );
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document.write( "4*4*4=64 three digit numbers that have all even digits.\r<BR>\n" );
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document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r<BR>\n" );
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document.write( "There are 4!/2!=12 ways to place the vowels on the ends:<BR>\n" );
document.write( "ae,ai,au,ea,ei,eu,ia,ie,iu,ua,ue,ui\r<BR>\n" );
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document.write( "Place them and arrange the 6 inside letters in 6!/2! ways.\r<BR>\n" );
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document.write( "We divide by 2 because of the repeated 't'.\r<BR>\n" );
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document.write( "So, the number of ways is 12*(6!/2!)=4320 ways </SPAN>\n" );
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