document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193292>Question 1193292</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 13 people want to play a game. There can be any number of people on each team but only 2 teams total. How many combinations of teams can be formed? \r<BR>\n" );
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document.write( "I need steps and answer using nCr formula. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #825305 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</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=825305\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The statement of the problem does not make it absolutely clear; but I will assume each of the 13 people is on one team or the other.<br><BR>\n" );
document.write( "So to form the teams, we can choose some number out of the 13 to be on one team, and the ones not chosen form the other team.<br><BR>\n" );
document.write( "For example, if the first team chosen has 5 players, then the number of ways of forming the two teams is 13C5.<br><BR>\n" );
document.write( "Then, since the first team chosen can have any number of players, the total number of ways of forming the two teams is<br><BR>\n" );
document.write( "13C0 + 13C1 + 13C2 +...+ 13C12 + 13C13 = 2^13 = 8192<br><BR>\n" );
document.write( "However, presumably a \"team\" with 0 players would not be considered a team, so the requirement of \"2 teams total\" would not be satisfied.  So the number of ways of forming 2 teams from 13 players (eliminating the cases where the first team is made up of either 0 or 13 players) is<br><BR>\n" );
document.write( "13C1 + 13C2 +...+ 13C12 = 8192-2 = 8190.<br><BR>\n" );
document.write( "ANSWER: 8190<br><BR>\n" );
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