document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=579315>Question 579315</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If there are a total of 14 players to choose from, how many ways can you pick your players if each team picks one at a time? (order does not matter) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #370944 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=370944\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> assume only 4 players.<BR>\n" );
document.write( "assume the players are a,b,c,d<BR>\n" );
document.write( "there are 6 teams composed of 2 players each that can be generated from a pool of 4 players.<BR>\n" );
document.write( "those teams are:<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\r<BR>\n" );
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document.write( "any one of these combinations can be chosen by either team leader depending on what the other team leader chose.\r<BR>\n" );
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document.write( "the team leader that picks first gets 4 * 2 = 8 possible choices.<BR>\n" );
document.write( "the team leader that picks second gets 3 * 1 = 3 possible choices.\r<BR>\n" );
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document.write( "the team leader who chooses first has a greater choice, but each team winds up with 2 players each regardless and the number of unique possible teams that can be formed is the same regardless of who picks first.\r<BR>\n" );
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document.write( "the formula for generating a team of 2 players out of 4 players is the combination formula of C(4,2) which becomes (4!) / (2!*2!) which becomes (4*3*2!) / (2*1*2!) which is equal to (4*3) / (2*1) which is equal to 6.<BR>\n" );
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document.write( "the formula for generating a team of 7 players out of 14 players is the combination formula of C(14,7) which becomes (14!) / (7!*7!) which becomes (14*13*12*11*10*9*8*7!) / (7*6*5*4*3*2*1*7!)<BR>\n" );
document.write( "the 7! in the numerator and the denominator cancel out and you are left with (14*13*12*11*10*9*8) / (7*6*5*4*3*2*1)<BR>\n" );
document.write( "this winds up being equal to 3432.<BR>\n" );
document.write( "3432 possible teams of seven players each can be generated from 14 players where each team contains 7 players.\r<BR>\n" );
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document.write( "the team leader who gets to choose first gets more choices than the team leader who gets to pick second.<BR>\n" );
document.write( "this works out as follows:<BR>\n" );
document.write( "team leader that picks first gets to choose:<BR>\n" );
document.write( "14 * 12 * 10 * 8 * 6 * 4 * 2 = 645120 possible choices.<BR>\n" );
document.write( "team leader that picks second gets to choose:<BR>\n" );
document.write( "13 * 11 * 9 * 7 * 5 * 3 * 1 = 135135 possible choices.<BR>\n" );
document.write( "there is a definite advantage to being able to choose first.\r<BR>\n" );
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document.write( "regardless of who picks first, the possible teams that can be generated that are unique where order doesn't count are calculated using the combination formula of C(14,7).\r<BR>\n" );
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document.write( "this is what i believe is the correct way to calculate this.\r<BR>\n" );
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document.write( "the problem statement is:<BR>\n" );
document.write( "If there are a total of 14 players to choose from, how many ways can you pick your players if each team picks one at a time? (order does not matter)\r<BR>\n" );
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document.write( "the question is difficult to answer because it is ambiguous.<BR>\n" );
document.write( "do they want the number of possible teams that can be generated that are unique or do they want the number of possible ways to choose the team?\r<BR>\n" );
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document.write( "the number of possible ways to pick a team are different depending on who chooses first and who chooses second.\r<BR>\n" );
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document.write( "the number of possible unique teams that can be formed is the same regardless of who picks first and who picks second.\r<BR>\n" );
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document.write( "i would go with the combination formula because that's what you are studying and they didn't differentiate between who picks first and who picks second in the question.\r<BR>\n" );
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document.write( "that's just a guess though.<BR>\n" );
document.write( "i have no idea what your instructor really wants.<BR>\n" );
document.write( "order does not matter means combination.<BR>\n" );
document.write( "order does matter means permutation.<BR>\n" );
document.write( "i think combination is what applies here.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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