document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1091481>Question 1091481</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many even three-digit numbers can be formed from the <BR>\n" );
document.write( "digits: 0, 1, 2, 3, 4, 5, 6 such that 5 is never placed <BR>\n" );
document.write( "in the tens position? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #706062 by </B><A HREF=/tutors/aboutme.mpl?userid=Gentle+Phill><B>Gentle Phill(18)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Gentle+Phill><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=Gentle+Phill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=706062\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> #Soln<BR>\n" );
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document.write( "Given d digits:<BR>\n" );
document.write( "0,1,2,3,4,5,6<BR>\n" );
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document.write( "To form even 3-digits without repitition & place of 50:<BR>\n" );
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document.write( "1. Nos must end with either 0,2,4,6<BR>\n" );
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document.write( "2. Nos must not Bgin with 0<BR>\n" );
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document.write( "3. By given rule, 5 must not appear in the middle<BR>\n" );
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document.write( "To ensure coverage for all of the above without contradiction, we must observe D many cases possible bit by bit<BR>\n" );
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document.write( "#Case_1: 0 as unit<BR>\n" );
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document.write( "When 0 is unit, any no. can occupy 1st spot:<BR>\n" );
document.write( "1_0<BR>\n" );
document.write( "2_0<BR>\n" );
document.write( "3_0<BR>\n" );
document.write( "4_0<BR>\n" );
document.write( "5_0<BR>\n" );
document.write( "6_0<BR>\n" );
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document.write( "However:<BR>\n" );
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document.write( "~ When 1,2,3,4 nd 6 re 1st digit, 5 is neva used. We'll've:<BR>\n" );
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document.write( "[5][4][1] = 20<BR>\n" );
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document.write( "Since 0 takes last spot, 1 of 5 nos takes 1st spot and 1 of d remainin 4 nos take 2nd spot<BR>\n" );
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document.write( "~ When 5 occupies 1st spot, we'll've:<BR>\n" );
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document.write( "[1][5][1] = 5<BR>\n" );
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document.write( "#Case_2: Either of 2,4,6 as unit<BR>\n" );
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document.write( "Digit could start with 1,3,5 & any other 2 even not used as unit<BR>\n" );
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document.write( "However:<BR>\n" );
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document.write( "~ When 5 isn't 1st digit, it isn't used at all:<BR>\n" );
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document.write( "[4][4][3] = 48<BR>\n" );
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document.write( "i.e<BR>\n" );
document.write( "[1,3 or any 2 even not used up][remaining 4 nos excluding '5'][2,4 or 6]<BR>\n" );
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document.write( "~ When 5 is used:<BR>\n" );
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document.write( "[1][5][3] = 15<BR>\n" );
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document.write( "i.e<BR>\n" );
document.write( "[only 5][any other 5 excluding used up evens][2,4,6]<BR>\n" );
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document.write( "Total = 20+5+48+15 = 88<BR>\n" );
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document.write( "Your friend,<BR>\n" );
document.write( "Francis. </SPAN>\n" );
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