document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=256382>Question 256382</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the formula for solving this? \"If you have a class consisting of 10 girls and 20 boys, in how many different ways can you form a committee from the class members such that there will be 2 girls and 2 boys on the committee?\" </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #188502 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=188502\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> formula is:\r<BR>\n" );
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document.write( "c(10,2) * c(20,2)\r<BR>\n" );
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document.write( "that's (10! / (2!8!)) * (20!/(2!18!))\r<BR>\n" );
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document.write( "that becomes:\r<BR>\n" );
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document.write( "(10*9/2*1) * (20*19/2*1) which equals 45*190 = 8550\r<BR>\n" );
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document.write( "to see this in action, assume this was 3 girls and 4 boys and you want a committee of 2 girls and 2 boys.\r<BR>\n" );
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document.write( "number of possible combinations for girls is c(3,2) = 3!/2!1! = 3\r<BR>\n" );
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document.write( "assume the girls are abc.\r<BR>\n" );
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document.write( "then you get possible combinations of:\r<BR>\n" );
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document.write( "ab<BR>\n" );
document.write( "ac<BR>\n" );
document.write( "bc\r<BR>\n" );
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document.write( "anything else would be a duplicate.   example:   ba is the same combination of ab because order is not considered.   if order was considered, it would be a permutation.\r<BR>\n" );
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document.write( "for the boys, the possible combinations would be c(4,2) = 4!/2!2! = 6\r<BR>\n" );
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document.write( "if the boys are defg, thenpossible combinations are:\r<BR>\n" );
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document.write( "de<BR>\n" );
document.write( "df<BR>\n" );
document.write( "dg<BR>\n" );
document.write( "ef<BR>\n" );
document.write( "eg<BR>\n" );
document.write( "fg\r<BR>\n" );
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document.write( "now, for each combination of girls, you get 6 combinations of boys, which means a total of:\r<BR>\n" );
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document.write( "c(3,2)*c(4,2) = 3 * 6 = 18\r<BR>\n" );
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document.write( "these combinations would be:\r<BR>\n" );
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document.write( "ab + de<BR>\n" );
document.write( "ab + df<BR>\n" );
document.write( "ab + dg<BR>\n" );
document.write( "ab + ef<BR>\n" );
document.write( "ab + eg<BR>\n" );
document.write( "ab + fg\r<BR>\n" );
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document.write( "ac + de<BR>\n" );
document.write( "ac + df<BR>\n" );
document.write( "ac + dg<BR>\n" );
document.write( "ac + ef<BR>\n" );
document.write( "ac + eg<BR>\n" );
document.write( "ac + fg\r<BR>\n" );
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document.write( "bc + de<BR>\n" );
document.write( "bc + df<BR>\n" );
document.write( "bc + dg<BR>\n" );
document.write( "bc + ef<BR>\n" );
document.write( "bc + eg<BR>\n" );
document.write( "bc + fg\r<BR>\n" );
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document.write( "same principle applies for the bigger figures, so your answer should be as stated above.\r<BR>\n" );
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document.write( "  </SPAN>\n" );
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