document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192101>Question 1192101</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a volleyball game, each team must play with all the other teams. How many games will there be?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #824002 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=824002\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i believe it will be a combination formula that allows you to find the answer to this.<BR>\n" );
document.write( "the formula is c(n,x).<BR>\n" );
document.write( "n is the number of teams<BR>\n" );
document.write( "x is the number of 2 team games.<BR>\n" );
document.write( "c(n,x) = n! / (x! * (n-x)!)<BR>\n" );
document.write( "the following excerpt from excel shows you how many games need to be played.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "n	x	c(n,x)\r\n" );
document.write( "2	2	1\r\n" );
document.write( "3	2	3\r\n" );
document.write( "4	2	6\r\n" );
document.write( "5	2	10\r\n" );
document.write( "6	2	15\r\n" );
document.write( "</PRE><BR>\n" );
document.write( "i'll use A, B, C, ..... to identify each team.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when n = 2 and x = 2, you get 1 game that needs to be played.<BR>\n" );
document.write( "that game is played between A and B, which will be shown as the set AB.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when n = 3, 3 games need to be played.<BR>\n" );
document.write( "they will be between:<BR>\n" );
document.write( "AB<BR>\n" );
document.write( "AC<BR>\n" );
document.write( "BC\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "what this means is:<BR>\n" );
document.write( "A plays with B<BR>\n" );
document.write( "B plays with C<BR>\n" );
document.write( "B plays with C\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if you look at it from the point of the team playing the other teams, you get:<BR>\n" );
document.write( "A plays with B and C<BR>\n" );
document.write( "B plays with A and C<BR>\n" );
document.write( "C plays with A and B\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when A plays with B, B is automatically playing with A.<BR>\n" );
document.write( "that's AB and BA equals the same game.<BR>\n" );
document.write( "that's what the combination formula does.<BR>\n" );
document.write( "it tells you how many sets of 2 you can get from a set of n when order doesn't matter.<BR>\n" );
document.write( "order doesn't matter means that AB and BA are the same set.<BR>\n" );
document.write( "if order matters, then AB and BA would be different sets.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when n = 4, the number of games that have to be played so each team plays with each other team would be (4,2) = 6.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that works out to be:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\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" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if you look at it from the standpoint of A, A plays with B, C, and D.<BR>\n" );
document.write( "if you look at it from the standpoint of B, B plays with A. C, and D.<BR>\n" );
document.write( "if you look at it from the standpoint of C, C plays with A, B, and D.<BR>\n" );
document.write( "if you look at it from the standpoint of D, D plays with A, B, and C.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "every team has played with every other team exactly 1 time.<BR>\n" );
document.write( "this occurs in 4 games.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the formula used is the combination formula.<BR>\n" );
document.write( "it tells you how many sets of x you can get from a set of n when order doesn't matter.<BR>\n" );
document.write( "when x = 2, then it's telling you how many sets of 2 you can get from a set of n when order doesn't matter.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "once again, order doesn't matter means that AB and BA are considered part of the same set and are only shown as either AB or BA, but not both.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "to show you the difference i will do C(4,2) and P(4,2).<BR>\n" );
document.write( "C(n,x) formula is n! / (x! * (n-x)!)<BR>\n" );
document.write( "P(n,x) formula is n! / (n-x)!)<BR>\n" );
document.write( "C(4,2) = 6<BR>\n" );
document.write( "P(4,2) = 12<BR>\n" );
document.write( "the number of combinations of sets of 2 from 4 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<BR>\n" );
document.write( "that's a total of 6.<BR>\n" );
document.write( "the number of permutations of sets of 2 from 4 are:<BR>\n" );
document.write( "AB, BA<BR>\n" );
document.write( "AC, CA<BR>\n" );
document.write( "AD. DA<BR>\n" );
document.write( "BC, CB<BR>\n" );
document.write( "BD, DB<BR>\n" );
document.write( "CD, DC<BR>\n" );
document.write( "that's 12.<BR>\n" );
document.write( "where AB and BA were considered part of the same set in C(4,2), AB and BA were considered part of different sets in P(4,2).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "with the combination formula, order doesn't matter.<BR>\n" );
document.write( "with the permutation formula, order does matter.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the number of games that must be played where each team plays each other team uses the combination formula.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's a reference that might help you to understand the difference.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.mathsisfun.com/combinatorics/combinations-permutations.html\" target = \"_blank\">https://www.mathsisfun.com/combinatorics/combinations-permutations.html</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "note that the combination and permutation formulas assume selections without replacement.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "note also that:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "C(n,x) = P(n,x) / x!<BR>\n" );
document.write( "P(n,x) = C(n,x) * x!\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );