document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=87547>Question 87547</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How may different 5-digit numbers that are odd and less than 50,000 can be formed using the digits 2,3,4,5,6,7 and 8 without repetition? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #258795 by </B><A HREF=/tutors/aboutme.mpl?userid=sudhanshu_kmr><B>sudhanshu_kmr(1152)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=sudhanshu_kmr><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=sudhanshu_kmr><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=258795\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> At unit place only one of these are possible 3,5,or 7.\r<BR>\n" );
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document.write( "Case A (when 3 at unit place i.e fifth position) : \r<BR>\n" );
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document.write( "for first position i.e  _xxxx only 2 or 4 is possible otherwise it will greater \r<BR>\n" );
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document.write( "than 50,000\r<BR>\n" );
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document.write( "so, no. of ways to fill first position  = 2  (two digits have used )\r<BR>\n" );
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document.write( "now, no. of ways to fill second position = 5    ( only 5 digits are remaining)\r<BR>\n" );
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document.write( "no. of ways to fill third position i.e xx_xx  = 4 (only 4 digits are remaining)\r<BR>\n" );
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document.write( "no. of ways to fill fourth position = 3     (only 3 digits are remaining)\r<BR>\n" );
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document.write( "fifth position is already occupied by 3.\r<BR>\n" );
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document.write( "so, total no. of different numbers that can be formed = 2 * 5 * 4 * 3 =120<BR>\n" );
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document.write( "Case B (when 5 at unit place i.e fifth position) : \r<BR>\n" );
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document.write( "for first position i.e  _xxxx only 2, 3 or 4 is possible otherwise it will \r<BR>\n" );
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document.write( "greater than 50,000\r<BR>\n" );
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document.write( "so, no. of ways to fill first position  = 3      (two digits have used )\r<BR>\n" );
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document.write( "now, no. of ways to fill second position = 5    ( only 5 digits are remaining)\r<BR>\n" );
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document.write( "no. of ways to fill third position i.e xx_xx  = 4 (only 4 digits are remaining)\r<BR>\n" );
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document.write( "no. of ways to fill fourth position = 3     (only 3 digits are remaining)\r<BR>\n" );
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document.write( "fifth position is already occupied by 5.\r<BR>\n" );
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document.write( "so, total no. of different numbers that can be formed = 3 * 5 * 4 * 3 =180\r<BR>\n" );
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document.write( "Case C (when 7 at unit place i.e fifth position) : \r<BR>\n" );
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document.write( "similarly,\r<BR>\n" );
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document.write( "so, no. of ways to fill first position  = 3      (two digits have used )\r<BR>\n" );
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document.write( "now, no. of ways to fill second position = 5    ( only 5 digits are remaining)\r<BR>\n" );
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document.write( "no. of ways to fill third position i.e xx_xx  = 4 (only 4 digits are remaining)\r<BR>\n" );
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document.write( "no. of ways to fill fourth position = 3     (only 3 digits are remaining)\r<BR>\n" );
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document.write( "fifth position is already occupied by 7.\r<BR>\n" );
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document.write( "so, total no. of different numbers that can be formed = 3 * 5 * 4 * 3 =180\r<BR>\n" );
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document.write( "now we add the value of these three  cases.\r<BR>\n" );
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document.write( "no. of different 5-digit numbers that are odd and less than 50,000 can be \r<BR>\n" );
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document.write( "formed    =  120 + 180 + 180  = 480\r<BR>\n" );
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document.write( "It is possible that some typing mistake in solution of a problem, if any please ignore it. Understand the concept and try to solve the problem yourself. If there is problem related to concept, contact at <BR>\n" );
document.write( "sudhanshu.cochin@yahoo.com or sudhanshu.cochin@gmail.com <BR>\n" );
document.write( "Best of luck....... \r<BR>\n" );
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document.write( "waiting for your reply......\r<BR>\n" );
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document.write( " </SPAN>\n" );
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