document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197425>Question 1197425</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (a) How many words can be formed using letter of PEPSUDENT using each letter at most once? <BR>\n" );
document.write( "   i) If each letter must be used, <BR>\n" );
document.write( "   ii) If some or all the letters may be omitted. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #830689 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=830689\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i) If each letter must be used\r<BR>\n" );
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document.write( "\"PEPSUDENT\" has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > letters, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > P, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > E, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > S, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+ ALIGN=MIDDLE  ALT=\"1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >U,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1+ ALIGN=MIDDLE  ALT=\"+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >D, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > N, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >T\r<BR>\n" );
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document.write( " there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" > distinct letters to use, and  if each letter must be used ones \r<BR>\n" );
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document.write( "that is \"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Position <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\" or \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7P7+=+7%2A6%2A5%2A4%2A3%2A2%2A1+=+5040 ALIGN=MIDDLE  ALT=\"7P7+=+7%2A6%2A5%2A4%2A3%2A2%2A1+=+5040\"   DISABLED_style= \"max-width:90%; height:auto;\" > ways  \r<BR>\n" );
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document.write( "Here's why that formula works:\r<BR>\n" );
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document.write( "Choose the 1st letter any of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7+ ALIGN=MIDDLE  ALT=\"7+\"   DISABLED_style= \"max-width:90%; height:auto;\" >ways.<BR>\n" );
document.write( "Choose the 2nd letter any of the remaining <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6+ ALIGN=MIDDLE  ALT=\"6+\"   DISABLED_style= \"max-width:90%; height:auto;\" >ways.<BR>\n" );
document.write( "Choose the 3rd letter any of the remaining <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > ways.<BR>\n" );
document.write( "Choose the 4th letter any of the remaining <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+ ALIGN=MIDDLE  ALT=\"4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >ways.<BR>\n" );
document.write( "Choose the 5th letter any of the remaining <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ways.<BR>\n" );
document.write( "Choose the 6th letter either of the remaining <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ways.<BR>\n" );
document.write( "Choose the 7th letter only the remaining <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > way.\r<BR>\n" );
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document.write( "That's <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7P7+=+7%2A6%2A5%2A4%2A3%2A2%2A1+=+7%21+=+5040 ALIGN=MIDDLE  ALT=\"7P7+=+7%2A6%2A5%2A4%2A3%2A2%2A1+=+7%21+=+5040\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "ii) If some or all the letters may be omitted.\r<BR>\n" );
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document.write( "That's \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7P0%2B7P1%2B7P2%2B7P3%2B7P4%2B7P5%2B7P6%2B7P7 ALIGN=MIDDLE  ALT=\"7P0%2B7P1%2B7P2%2B7P3%2B7P4%2B7P5%2B7P6%2B7P7\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "or<BR>\n" );
document.write( "       <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B7%2B42%2B210%2B840%2B2520%2B5040%2B5040+=+13699 ALIGN=MIDDLE  ALT=\"1%2B7%2B42%2B210%2B840%2B2520%2B5040%2B5040+=+13699\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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