document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=195613>Question 195613</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is not from a text book but a question my instructor posed to me.  I am not sure how to figure it out.  Can someone please help me with it?\r<BR>\n" );
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document.write( "Suppose we have a list of zip codes that is only the 5-digit without the extension and there is no replacement or repetition. How many possible zip codes do we have?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #146702 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=146702\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Note: I'm assuming that zero can be used as the first digit.\r<BR>\n" );
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document.write( "Method # 1:\r<BR>\n" );
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document.write( "Number of Possible Permutations = Number of Choices 1st Digit * Number of Choices 2nd Digit * Number of Choices 3rd Digit * Number of Choices 4th Digit * Number of Choices 5th Digit\r<BR>\n" );
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document.write( "Number of Possible Permutations = 10 * 9 * 8 * 7 * 6\r<BR>\n" );
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document.write( "Number of Possible Permutations = 30,240\r<BR>\n" );
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document.write( "So there are 30,240 different zip codes\r<BR>\n" );
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document.write( "Method # 2\r<BR>\n" );
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document.write( "Since there are 10 possible numbers to choose from and there are 5 positions to place them in, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=10 ALIGN=MIDDLE  ALT=\"n=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=5 ALIGN=MIDDLE  ALT=\"r=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since order does matter, we must use the <a  rel=nofollow HREF=http://www.mathwords.com/p/permutation_formula.htm>permutation formula</a>:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{n}P_{r}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%21%2F%28n-r%29%21 ALIGN=MIDDLE  ALT=\"n%21%2F%28n-r%29%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{10}P_{5}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%21%2F%2810-5%29%21 ALIGN=MIDDLE  ALT=\"10%21%2F%2810-5%29%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=10 ALIGN=MIDDLE  ALT=\"n=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=5 ALIGN=MIDDLE  ALT=\"r=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{10}P_{5}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%21%2F5%21 ALIGN=MIDDLE  ALT=\"10%21%2F5%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10-5 ALIGN=MIDDLE  ALT=\"10-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 5\r<BR>\n" );
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document.write( "Expand 10!<BR>\n" );
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document.write( "Expand 5!<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{10}P_{5}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F%285%2A4%2A3%2A2%2A1%29 ALIGN=MIDDLE  ALT=\"%2810%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F%285%2A4%2A3%2A2%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{10}P_{5}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%2A9%2A8%2A7%2A6%2Across%285%2A4%2A3%2A2%2A1%29%29%2F%28cross%285%2A4%2A3%2A2%2A1%29%29 ALIGN=MIDDLE  ALT=\"%2810%2A9%2A8%2A7%2A6%2Across%285%2A4%2A3%2A2%2A1%29%29%2F%28cross%285%2A4%2A3%2A2%2A1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Cancel\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{10}P_{5}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2A9%2A8%2A7%2A6 ALIGN=MIDDLE  ALT=\"10%2A9%2A8%2A7%2A6\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{10}P_{5}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30240 ALIGN=MIDDLE  ALT=\"30240\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Now multiply 10*9*8*7*6 to get 30,240\r<BR>\n" );
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document.write( "So 10 choose 5 (where order does matter) yields 30,240 unique permutations\r<BR>\n" );
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document.write( "So once again, there are 30,240 different zip codes.<BR>\n" );
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