document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=30425>Question 30425</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the number of different 7 digit numbers that can be made by rearranging the digits 3053354? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #17087 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=17087\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if all the numbers were different, we would have 7! permutations... which is 5040 different numbers.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Additional thing to think about would be numbers like 0123456.. this is not a recognised number, so we cannot have the zero in the \"first position\".\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So... <BR>\n" );
document.write( "First position: how many numbers could we have? Answer is 6 (as the zero is not allowed there).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Second position: how many numbers? Well any of the 6 remaining.<BR>\n" );
document.write( "Third position: Any of the 5 remaining<BR>\n" );
document.write( "fourth position: Any of the 4 remaining<BR>\n" );
document.write( "and so on.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Total: 6*6*5*4*3*2*1 --> 6*6! --> 6*720 --> 4320.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Notice, this is 720 less than 5040 ie it is one whole block of 6!\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now, this is not the final answer, since there are three 3's and two 5's, so there is going to be repetition of certain numbers.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Total number of different numbers = 4320/(3!2!)<BR>\n" );
document.write( "Total number of different numbers = 4320/(6*2)<BR>\n" );
document.write( "Total number of different numbers = 4320/12<BR>\n" );
document.write( "Total number of different numbers = 360\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So, there are just 360 different numbers that can be made up from the given set of digits.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "jon.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );