document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182131>Question 1182131</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I saw this solution online from a tutor (ikelyn). I think there's a mistake in it and i need to make sure I'm right. So in case b in this solution. Shouldn't the equation be 8*8*7*4 = 1792? (4 because there are 4 different possible digits?) In the solution it says 8*8*7 = 448. \r<BR>\n" );
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document.write( "The solution:\r<BR>\n" );
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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 ?\r<BR>\n" );
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document.write( "Solution\r<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<BR>\n" );
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document.write( "In my solution, I will consider two cases separately:\r<BR>\n" );
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document.write( "        case (a):  the last digit is 0 (zero),\r<BR>\n" );
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document.write( "    and\r<BR>\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<BR>\n" );
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document.write( "Case (a):   the last digit is  0  (zero)\r<BR>\n" );
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document.write( "    Then the first (most-left) digit is any of 9 remaining digits;\r<BR>\n" );
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document.write( "         the second digit is any of remaining 8 digits;\r<BR>\n" );
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document.write( "         the third digit is any of remaining 7 digits.\r<BR>\n" );
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document.write( "    So, the total number of possible options is  9*8*7 = 504 in this case.\r<BR>\n" );
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document.write( "Case (b):   the last digit is any of remaining  4  digits  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<BR>\n" );
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document.write( "         the second digit is any of 8 remaining digits (zero is ALLOWED in this position);\r<BR>\n" );
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document.write( "         the third digit  is any of 7 remaining digits (zero is ALLOWED in this position).\r<BR>\n" );
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document.write( "    So, the total number of possible options is  8*8*7 = 448 in this case.\r<BR>\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( "ANSWER.  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. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #812100 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=812100\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Yes you are correct. \r<BR>\n" );
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document.write( "There are 8 choices for slot one, 8 for slot two, 7 for slot three, and 4 choices for the last slot.\r<BR>\n" );
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document.write( "So the final answer would be 504+1792 = 2296<BR>\n" );
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document.write( " </SPAN>\n" );
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