document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1104768>Question 1104768</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many ways are there to create a 6 digit pin number where exactly 4 of digits are the same? the numbers 0-9 can be in any place </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #719644 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=719644\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "I have a completely different interpretation of the problem, and a completely different answer, than the other tutor....<br><BR>\n" );
document.write( "(1) You can choose any 1 of 10 digits to be the one that occurs 4 times: C(10,1) = 10.<BR>\n" );
document.write( "(2) You need to choose 2 of the other 9 digits for the other 2 digits of the PIN: C(9,2) = 36.<BR>\n" );
document.write( "(3) The number of different ways you can arrange the 4 identical and 2 other digits is (6!)/(4!) = 720/24 = 30.<br><BR>\n" );
document.write( "The total number of different PINs is 10*36*30 = 10800. </SPAN>\n" );
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