document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204021>Question 1204021</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In how many ways can a class of 16 students be assigned 2 A's, 6 B's, 3 C's, 2 D's and 3 F's?<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 #840025 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=840025\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "In solving a problem like this, it is useful to know that the different grades can be assigned in any order; the result will be the same.  For example, if the grades are assigned from lowest (F) to highest (A), then the calculation is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2816%2C3%29%2AC%2813%2C2%29%2AC%2811%2C3%29%2AC%288%2C6%29%2AC%282%2C2%29=%28560%29%2878%29%28165%29%2828%29%281%29=201801600 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Of course the last factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%282%2C2%29 ALIGN=MIDDLE  ALT=\"C%282%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not needed -- but showing it makes the complete process more clear.<br><BR>\n" );
document.write( "And a third way to find the answer to the question is to count the number of different ways of arranging the 16 grades in a string:<br><BR>\n" );
document.write( "AABBBBBBCCCDDFFF<br><BR>\n" );
document.write( "By a well-known counting principle, the number of distinct arrangements of those letters is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%21%2F%28%282%21%29%286%21%29%283%21%29%282%21%29%283%21%29%29=201801600 ALIGN=MIDDLE  ALT=\"16%21%2F%28%282%21%29%286%21%29%283%21%29%282%21%29%283%21%29%29=201801600\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
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