document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=668552>Question 668552</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help!\r<BR>\n" );
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document.write( "  Use a tree diagram showing all possible results when four fair coins are tossed.  then list the ways of getting exactly two tails.<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 #415662 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=415662\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Start with your two possibilities {H,T}\r<BR>\n" );
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document.write( "From each node in your tree sprout another two branches {H,T} until you've done this process 4 times. As a check, you should have 16 end possibilities. As 2^4 = 16.\r<BR>\n" );
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document.write( "Then, find the paths in your tree such that T only appears twice. You should get (from top to bottom:\r<BR>\n" );
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document.write( "{HHTT}<BR>\n" );
document.write( "{HTHT}<BR>\n" );
document.write( "{HTTH}<BR>\n" );
document.write( "{THHT}<BR>\n" );
document.write( "{THTH}<BR>\n" );
document.write( "{TTHH}\r<BR>\n" );
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document.write( "6 possibilities.\r<BR>\n" );
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document.write( "This makes sense because if we have 4 slots to choose from and we need 2 to be tails, there are exactly (4 choose 2) =  4!/2!*2! = 24/4 = 6 ways to do that. </SPAN>\n" );
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