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 #825368 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=825368\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Label the two teams as A and B.\r<BR>\n" );
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document.write( "Imagine we have 13 slots to represent the players. Each slot will be labeled either A or B.\r<BR>\n" );
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document.write( "Since we have 13 slots, and two choices per slot, this gives 2^13 = 8192 different ways to assign each player to a certain team. You can think of each slot like a binary light switch that turns on or off (for team A or team B).\r<BR>\n" );
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document.write( "If we require that each team needs 1 or more players, then we'd have to eliminate these cases:<ul><li>Everyone going to team A (since team B wouldn't have anyone)</li><li>Everyone going to team B (since team A wouldn't have anyone)</li></ul>That means we've eliminated 2 cases to drop the count to 8192-2 = 8190\r<BR>\n" );
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document.write( "As you can see, there isn't a need to involve the nCr combination formula. <BR>\n" );
document.write( "Though as the other tutor @greenestamps indirectly pointed out, summing all the terms along any row of Pascal's Triangle will yield a power of 2. Terms inside the triangle are directly connected to the nCr combination formula.\r<BR>\n" );
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document.write( "Answer: 8190<BR>\n" );
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