document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1081901>Question 1081901</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find how many no between 5000 and 6000 can be formed from the digits 1,2,3,4,5,6 <BR>\n" );
document.write( "a) if no digits are repeated<BR>\n" );
document.write( "b) if repeated digits are allowed </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #695937 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=695937\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Part (a)\r<BR>\n" );
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document.write( "The number must be between 5000 and 6000 so the number must start with 5. Any other starting point and we're not between 5000 and 6000. \r<BR>\n" );
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document.write( "If we pull out the digit '5', we're left with 5 other choices: 1,2,3,4,6\r<BR>\n" );
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document.write( "Imagine that the four digit number is composed of 4 slots A through D. The first slot A is locked in at 5. The other 3 slots (slot B,C,D) can change. \r<BR>\n" );
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document.write( "Slot B has 5 choices<BR>\n" );
document.write( "Once we make a choice, we have 4 choices left for slot C<BR>\n" );
document.write( "Slot D will have 3 choices\r<BR>\n" );
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document.write( "Overall, there are 5*4*3 = 60 different permutations when it comes to picking 3 items from a set of 5. \r<BR>\n" );
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document.write( "The answer to part (a) is <font size=4 color=red>60</font>\r<BR>\n" );
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document.write( "Part (b)\r<BR>\n" );
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document.write( "Repeats are allowed now so we can reuse the digit '5' if we want to. There are still 3 slots to fill since the first slot is locked to be 5 (see explanation above).\r<BR>\n" );
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document.write( "The slots that aren't locked up (B through D) each have 6 choices giving 6*6*6 = 6^3 = 216 different three-digit combinations\r<BR>\n" );
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document.write( "So there are 216 different numbers we can form that are between 5000 and 6000.\r<BR>\n" );
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document.write( "The answer to part (b) is <font size=4 color=red>216</font> </SPAN>\n" );
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