document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=167633>Question 167633</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The neighborhood association elects a president, vice president, secretary and treasurer.How many sets of officers are possible if there are 16 people in the association? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #123524 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=123524\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you can make (16*15*14*13)/(1*2*3*4) possible combinations of 4 people out of 16 people.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "this is the same as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816%21%29%2F%28%2812%21%29%2A%284%21%29%29 ALIGN=MIDDLE  ALT=\"%2816%21%29%2F%28%2812%21%29%2A%284%21%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where 16 = number of people in universe to pick from (n),<BR>\n" );
document.write( "and 4 = number of people you want in each set (x)<BR>\n" );
document.write( "general formula is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%21%29%2F%28%28%28n-x%29%21%29%2A%28x%21%29%29 ALIGN=MIDDLE  ALT=\"%28n%21%29%2F%28%28%28n-x%29%21%29%2A%28x%21%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the number comes out to be 1820 possible sets of 4 out of 16 people.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "what is happening is easier to see if the universe is smaller.<BR>\n" );
document.write( "say you wanted a set of 2 people out of a universe of 3 people.<BR>\n" );
document.write( "n = 3<BR>\n" );
document.write( "x = 2<BR>\n" );
document.write( "n!/(1!*2!) = 3*2*1/1*2*1 = 3<BR>\n" );
document.write( "there are 3 possible sets of 2 out of 3.<BR>\n" );
document.write( "assuming the elements in the universe are abc, then the possible combinations are:<BR>\n" );
document.write( "ab<BR>\n" );
document.write( "ac<BR>\n" );
document.write( "bc<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "if you wanted 2 out of 4, then the number of possible sets would be<BR>\n" );
document.write( "4! / (2!*2!) = 4*3*2*1/2*1*2*1 = 6<BR>\n" );
document.write( "assuming elements in your universe are abcd, then<BR>\n" );
document.write( "elements in each set would be:<BR>\n" );
document.write( "ab<BR>\n" );
document.write( "ac<BR>\n" );
document.write( "ad<BR>\n" );
document.write( "bc<BR>\n" );
document.write( "bd<BR>\n" );
document.write( "cd<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "your problem is much more complex but solves using the same method.<BR>\n" );
document.write( "let's say your universe was abcdefghijklmnop<BR>\n" );
document.write( "then possible sets of 4 would be<BR>\n" );
document.write( "abcd<BR>\n" );
document.write( "abce<BR>\n" );
document.write( "abcf<BR>\n" );
document.write( "abcg<BR>\n" );
document.write( "etc.,<BR>\n" );
document.write( "all the way through to...<BR>\n" );
document.write( "lmno<BR>\n" );
document.write( "lmnp<BR>\n" );
document.write( "mnop<BR>\n" );
document.write( "-----\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );