document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1026955>Question 1026955</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A six digit number is to be formed using only digits from the set {1,2,3,5,6,7,9}. There are to be three distinct digits in the numbers formed, one of which appears four times and the other two, once each. How many different numbers are possible. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #642233 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=642233\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Choose the digit that appears four times (7 ways), then choose the remaining two digits (say A and B). Assume that A and B are chosen with order important (6*5 = 30 ways) - you will see why later.\r<BR>\n" );
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document.write( "Choose four of the six placeholders for the digit that appears four times to occupy (6C4 = 15 ways). Then put A (the first of the 2 digits chosen) in the first unoccupied spot and B in the second unoccupied spot. This constructs such a number, and we know that we didn't overcount.\r<BR>\n" );
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document.write( "# of ways = 7*30*15 = 3150\r<BR>\n" );
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