document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208471>Question 1208471</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One of the educational sites on the Internet requires the creation of<BR>\n" );
document.write( "User account protected with 8 characters password<BR>\n" );
document.write( "Different Choose from letters: A, B, C, D, E, F<BR>\n" );
document.write( "And numbers: 6 , 5 , 4 , 3 , 2 , 1, find the number of passwords that<BR>\n" );
document.write( "They can be created in the following cases:<BR>\n" );
document.write( "The password contains 4 numbers and 4 letters combined together  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #846901 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=846901\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "\"... 4 numbers and 4 letters combined together\" implies that any of the 8 characters chosen could be in any of the 8 positions.  So...<br><BR>\n" );
document.write( "(1) Choose 4 of the 6 letters in C(6,4) = 15 ways<BR>\n" );
document.write( "(2) Choose 4 of the 6 digits in C(6,4) = 15 ways<BR>\n" );
document.write( "(3) Order the 8 characters in 8! = 40320 ways<br><BR>\n" );
document.write( "Number of different passwords: 15*15*40320 = 9072000<br><BR>\n" );
document.write( "ANSWER: 9072000<br><BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );