document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=568942>Question 568942</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In how many ways can double game of tennis be arranged from eight boys and four girls if each side must have one boy and one girl?\r<BR>\n" );
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document.write( "Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #367174 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=367174\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> each side must have 1 boy and 1 girl.<BR>\n" );
document.write( "this makes the number of possible teams equal to 4 * 8 = 32.<BR>\n" );
document.write( "each girl can be paired with any of the 8 boys.\r<BR>\n" );
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document.write( "it takes 2 teams to play a game.<BR>\n" );
document.write( "the games can be arranged in 32 * 31 / 2 = 496 ways.<BR>\n" );
document.write( "32 * 31 / 2 is the combination formula of 32C2.\r<BR>\n" );
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document.write( "this would be easier to actually show what happens if there were less boys and girls.\r<BR>\n" );
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document.write( "assume there were 2 girls and 3 boys<BR>\n" );
document.write( "identify the girls by the letter a and b<BR>\n" );
document.write( "identify the boys by the numbers 1 and 2 and 3.<BR>\n" );
document.write( "there are 2 * 3 = 6 possible teams.<BR>\n" );
document.write( "those teams are<BR>\n" );
document.write( "a1<BR>\n" );
document.write( "a2<BR>\n" );
document.write( "a3<BR>\n" );
document.write( "b1<BR>\n" );
document.write( "b2<BR>\n" );
document.write( "b3<BR>\n" );
document.write( "it takes 2 teams to play a game.<BR>\n" );
document.write( "the number of possible games where each time plays each other team only once would be given by the formula 6C2 which results in 6 * 5 / 2 which results in 15 possible games.<BR>\n" );
document.write( "the possible games to be arranged would be as follows:<BR>\n" );
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document.write( "a1 plays a2<BR>\n" );
document.write( "a1 plays a3<BR>\n" );
document.write( "a1 plays b1<BR>\n" );
document.write( "a1 plays b2<BR>\n" );
document.write( "a1 plays b3<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "a2 plays a3<BR>\n" );
document.write( "a2 plays b1<BR>\n" );
document.write( "a2 plays b2<BR>\n" );
document.write( "a2 plays b3<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "a3 plays b1<BR>\n" );
document.write( "a3 plays b2<BR>\n" );
document.write( "a3 plays b3<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "b1 plays b2<BR>\n" );
document.write( "b1 plays b3<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "b2 plays b3<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the formula can be shown to be applicable with 2 girls and 3 boys.<BR>\n" );
document.write( "the same formula is used with 4 girls and 8 boys to get the answer provided above.<BR>\n" );
document.write( "number of possible teams if 4 * 8 = 32<BR>\n" );
document.write( "number of possible games is 32C2 which is equal to 32 * 31 / 2 = 496.<BR>\n" );
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