document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170640>Question 1170640</A>: <I><SPAN STYLE=\"word-break: break-all;\">  How many 4 - digit even numbers can be formed from<BR>\n" );
document.write( "the digits 0 to 9 if each digit is to be used only once in<BR>\n" );
document.write( "each number ?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #795513 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52803)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=795513\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "How many 4-digit even numbers can be formed from the digits 0 to 9 <BR>\n" );
document.write( "if each digit is to be used only once in each number ?<BR>\n" );
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document.write( "The fact that the number is an EVEN number means that the last digit is one of 5 even digits 0, 2, 4, 6, or 8.\r\n" );
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document.write( "In my solution, I will consider two cases separately:\r\n" );
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document.write( "        case (a):  the last digit is 0 (zero),\r\n" );
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document.write( "    and\r\n" );
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document.write( "        case (b): the last digit is any of the remaining 4 even digits 2, 4, 6 or 8.\r\n" );
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document.write( "<U>Case (a)</U>: &nbsp;&nbsp;the last digit is &nbsp;0 &nbsp;(zero)\r<BR>\n" );
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document.write( "    Then the first (most-left) digit is any of 9 remaining digits;\r\n" );
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document.write( "         the second digit is any of remaining 8 digits;\r\n" );
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document.write( "         the third digit is any of remaining 7 digits.\r\n" );
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document.write( "    So, the total number of possible options is  9*8*7 = 504 in this case.\r\n" );
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document.write( "<U>Case (b)</U>: &nbsp;&nbsp;the last digit is any of remaining &nbsp;4 &nbsp;digits &nbsp;2, 4, 6 or 8.\r<BR>\n" );
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document.write( "    Then the first (most-left) digit is any of 8 remaining digits (keep in mind that the leading digit CAN NOT be 0 (!));\r\n" );
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document.write( "         the second digit is any of 8 remaining digits (zero is ALLOWED in this position);\r\n" );
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document.write( "         the third digit  is any of 7 remaining digits (zero is ALLOWED in this position).\r\n" );
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document.write( "    So, the total number of possible options is  8*8*7 = 448 in this case.\r\n" );
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document.write( "Thus the total number of possibilities is 504 + 448 = 952.\r<BR>\n" );
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document.write( "<U>ANSWER</U>.  952 four-digit even numbers can be formed from the digits 0 to 9 if each digit is to be used only once in each number.<BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "The major lesson to learn from my solution is splitting the analysis in two cases.\r<BR>\n" );
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