document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=731622>Question 731622</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i have been doing combinations,and i have researched about subsets? and i found out that subsets are 2 to the power n but now i have a question ,given a subset ,how do you find the possible outcomes of choosing a specific number,ie (1,2,3,5,5,6,7,8,9,10,11) ,how many subsets contain the number 5 how many subsets  contain exactly three elements, one of which is 3  <BR>\n" );
document.write( "d.  contain exactly five elements, but neither 3 nor <BR>\n" );
document.write( " and the question gets complex when it says such,please help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #447816 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=447816\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The number of subsets with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n-1 ALIGN=MIDDLE  ALT=\"n-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > elements from a set with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > elements is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5En-2=2%282%5E%28n-1%29-1%29%7D%7D.+If+you+count+the+empty+set+and++the+whole+set+of+%7B%7B%7Bn ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > elements, there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5En ALIGN=MIDDLE  ALT=\"2%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" > subsets.<BR>\n" );
document.write( " <BR>\n" );
document.write( "How many subsets of {1,2,3,4,5,6,7,8,9,10,11} contain the number 5?<BR>\n" );
document.write( "One of those subsets will be {5}, with just one element.<BR>\n" );
document.write( "If you remove the number 5 from each of the subsets containing 5, you would get all the subsets of {1,2,3,4,6,7,8,9,10,11} and there is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E10-2 ALIGN=MIDDLE  ALT=\"2%5E10-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E10 ALIGN=MIDDLE  ALT=\"2%5E10\"   DISABLED_style= \"max-width:90%; height:auto;\" > of those (counting the empty set and the whole 10-element {1,2,3,4,6,7,8,9,10,11} set<BR>\n" );
document.write( "That is the number of subsets containing 5, counting {5} and  {1,2,3,4,5,6,7,8,9,10,11}.<BR>\n" );
document.write( " <BR>\n" );
document.write( "How many subsets of {1,2,3,4,5,6,7,8,9,10,11} contain exactly three elements, one of which is 3?<BR>\n" );
document.write( "Removing 3 from each of those subsets would give you all the subsets of {1,2,4,5,6,7,8,9,10,11} with exactly 2 elements and that is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2A9%2F2=5%2A9=45 ALIGN=MIDDLE  ALT=\"10%2A9%2F2=5%2A9=45\"   DISABLED_style= \"max-width:90%; height:auto;\" > subsets. There are several different combination symbols for that and you know which one you are expected to use.<BR>\n" );
document.write( " <BR>\n" );
document.write( "How many subsets of {1,2,3,4,5,6,7,8,9,10,11} have 5 elements but contain neither 3 not 5?<BR>\n" );
document.write( "All of those subsets can be made from {1,2,4,6,7,8,9,10,11} and there is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2A8%2A7%2A6%2A5%2F2%2F3%2F4%2F5=126 ALIGN=MIDDLE  ALT=\"9%2A8%2A7%2A6%2A5%2F2%2F3%2F4%2F5=126\"   DISABLED_style= \"max-width:90%; height:auto;\" > of them. </SPAN>\n" );
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