document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1131701>Question 1131701</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many possible distinct permutations using four of the letters in the word NIGERIA? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #748368 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=748368\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Breaking down the numbers into two cases, we can add the two counts:<BR>\n" );
document.write( "1.  Those with one \"I\" and<BR>\n" );
document.write( "2.  Those with two \"I\"s <br>\r<BR>\n" );
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document.write( "With one \"I\":<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%286C4%29%2A4%21+=+15%2A24+=+360+ ALIGN=MIDDLE  ALT=\"+%286C4%29%2A4%21+=+15%2A24+=+360+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "With two \"I\"s:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%285C2%29%2A%283C2%29%2A2%21+%2B+%285C2%29%2A3%21+=+60+%2B+60+=+120+ ALIGN=MIDDLE  ALT=\"+%285C2%29%2A%283C2%29%2A2%21+%2B+%285C2%29%2A3%21+=+60+%2B+60+=+120+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "(First term is where the two I's are separated by at least one letter and<BR>\n" );
document.write( "the 2nd term is where the two I's are together, the 5C2 arises because we <BR>\n" );
document.write( "have already selected two Is and now are free to choose 2 of the remaining <BR>\n" );
document.write( "5 letters) <br>\r<BR>\n" );
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document.write( "Adding gives 360+120 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%28+480+%29+ ALIGN=MIDDLE  ALT=\"+highlight%28+480+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > distinct permutations\r<BR>\n" );
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document.write( "--------<BR>\n" );
document.write( "Caution: Tutor MathLover's answer does not take into account the two \"I\"s.<BR>\n" );
document.write( " Therefore the answer she has arrived at has overcounted the number of <BR>\n" );
document.write( "unique permutations.  \r<BR>\n" );
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document.write( "  <BR>\n" );
document.write( " </SPAN>\n" );
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