document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=153019>Question 153019</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.  Suppose you use five different letters to make a computer password.  Find the number of possible five letter passwords.<BR>\n" );
document.write( "I got 11,881,376 using the formula  26 C 5.  Is this correct?\r<BR>\n" );
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document.write( "2. How many different ways can someone arrange 8 books on a shelf?  I got 64.\r<BR>\n" );
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document.write( "3.  If the first three digits of someone's phone number (no area code) are 555, how many different phone numbers could they have?  I got 11,881,373<BR>\n" );
document.write( "I used 26 to the 5th power.  \r<BR>\n" );
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document.write( "Thanks for your help.<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 #112471 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=112471\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) Here's a good question: is the password \"pass\" different from \"ssap\"? Since it is, this means that order matters. \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 permutation formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{26}P_{5}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=26%21%2F%2826-5%29%21 ALIGN=MIDDLE  ALT=\"26%21%2F%2826-5%29%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=26 ALIGN=MIDDLE  ALT=\"n=26\"   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{_{26}P_{5}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=26%21%2F21%21 ALIGN=MIDDLE  ALT=\"26%21%2F21%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=26-5 ALIGN=MIDDLE  ALT=\"26-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 21\r<BR>\n" );
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document.write( "Expand 26!<BR>\n" );
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document.write( "Expand 21!<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{26}P_{5}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2826%2A25%2A24%2A23%2A22%2A21%2A20%2A19%2A18%2A17%2A16%2A15%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F%2821%2A20%2A19%2A18%2A17%2A16%2A15%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29 ALIGN=MIDDLE   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{_{26}P_{5}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2826%2A25%2A24%2A23%2A22%2Across%2821%2A20%2A19%2A18%2A17%2A16%2A15%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%29%2F%28cross%2821%2A20%2A19%2A18%2A17%2A16%2A15%2A14%2A13%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%29 ALIGN=MIDDLE   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{_{26}P_{5}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=26%2A25%2A24%2A23%2A22 ALIGN=MIDDLE  ALT=\"26%2A25%2A24%2A23%2A22\"   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{_{26}P_{5}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7893600 ALIGN=MIDDLE  ALT=\"7893600\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Now multiply 26*25*24*23*22 to get 7,893,600\r<BR>\n" );
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document.write( "So there are 7,893,600 possible passwords\r<BR>\n" );
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document.write( "2)\r<BR>\n" );
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document.write( "If order does matter, then the number of combinations is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%21=8%2A7%2A6%2A5%2A4%2A3%2A2%2A1=40320 ALIGN=MIDDLE  ALT=\"8%21=8%2A7%2A6%2A5%2A4%2A3%2A2%2A1=40320\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So there are 40,320 ways to rearrange the books\r<BR>\n" );
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document.write( "3)\r<BR>\n" );
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document.write( "Let's say that the format is \r<BR>\n" );
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document.write( "(555)-xxx-xxxx\r<BR>\n" );
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document.write( "So we have 7 slots we're dealing with. This means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=7 ALIGN=MIDDLE  ALT=\"r=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Since we have 10 numbers to choose from, this tells us 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;\" > (note: the \"26\" that you used implies that you'll be using letters). Also, because order matters, 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 permutation formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{10}P_{7}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%21%2F%2810-7%29%21 ALIGN=MIDDLE  ALT=\"10%21%2F%2810-7%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=7 ALIGN=MIDDLE  ALT=\"r=7\"   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_{7}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%21%2F3%21 ALIGN=MIDDLE  ALT=\"10%21%2F3%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10-7 ALIGN=MIDDLE  ALT=\"10-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 3\r<BR>\n" );
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document.write( "Expand 10!<BR>\n" );
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document.write( "Expand 3!<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{10}P_{7}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%2A9%2A8%2A7%2A6%2A5%2A4%2Across%283%2A2%2A1%29%29%2F%28cross%283%2A2%2A1%29%29 ALIGN=MIDDLE  ALT=\"%2810%2A9%2A8%2A7%2A6%2A5%2A4%2Across%283%2A2%2A1%29%29%2F%28cross%283%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_{7}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2A9%2A8%2A7%2A6%2A5%2A4 ALIGN=MIDDLE  ALT=\"10%2A9%2A8%2A7%2A6%2A5%2A4\"   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_{7}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=604800 ALIGN=MIDDLE  ALT=\"604800\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Now multiply 10*9*8*7*6*5*4 to get 604,800\r<BR>\n" );
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document.write( "So there are 604,800 unique phone numbers to choose from.\r<BR>\n" );
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