document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1020987>Question 1020987</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If no digit is repeated in any number, how many four-digit numbers can be formed out of the digits 1, 2, 3, 4, 5, 6, 7? How many of these numbers will exceed 4000? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #636813 by </B><A HREF=/tutors/aboutme.mpl?userid=mathmate><B>mathmate(429)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathmate><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=mathmate><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=636813\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  <BR>\n" );
document.write( "Question:<BR>\n" );
document.write( "If no digit is repeated in any number, how many four-digit numbers can be formed out of the digits 1, 2, 3, 4, 5, 6, 7? How many of these numbers will exceed 4000?<BR>\n" );
document.write( " <BR>\n" );
document.write( "Solution:<BR>\n" );
document.write( "with no repetition, there are 7 choices for the first digit, 6 for the second, 5 for the third and 4 for the fourth for a total of 7*6*5*4=840 numbers.<BR>\n" );
document.write( "If the number must exceed 4000, then the first digit must be 4,5,6,or 7.<BR>\n" );
document.write( "Following the same logic above, there are 4*6*5*4=480 distinct numbers.  However, since 4000 does not exceed 4000, so it must be subtracted from the list leaving 480-1=479 numbers.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );