document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194947>Question 1194947</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this word problem using Combinations:\r<BR>\n" );
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document.write( "A quiz team of 5 children is to be selected from a class of 24 children. There are 14 girls and 10 boys in the class.<BR>\n" );
document.write( "(a) How many teams made up of 3 girls and 2 boys can be selected?<BR>\n" );
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document.write( "(b) How many teams can be selected with at least 3 girls?<BR>\n" );
document.write( " teams </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #827257 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=827257\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> there are 14 girls and 11 boys.<BR>\n" );
document.write( "the number of ways you can get a team of 5 children where 3 are girls and 2 are boys is equal to c(14,3) * c(11,2) = 20,020.<BR>\n" );
document.write( "the number of ways you can get a team of 5 children where at least 3 are girls is equal to c(14,3) * c(11,2) + c(14,4) + c(11,1) + c(14,5) * c(11,0) = 20,020 + 11,011 + 2,002 = 33,033.<BR>\n" );
document.write( "c(n,x) is equal to n! / (x! * (n-x)!)<BR>\n" );
document.write( "for example:<BR>\n" );
document.write( "c(14,3) = 14! / (3! * 11!) which is equal to:<BR>\n" );
document.write( "(14 * 13 * 12 * 11!) / (3! * 11!) which is equal to:<BR>\n" );
document.write( "(14 * 13 * 12) / (3 * 2 * 1) which is equal to:<BR>\n" );
document.write( "2184 / 6 which is equal to 364.<BR>\n" );
document.write( "and:<BR>\n" );
document.write( "c(11,2) = 11! / (2! * 9!) which is equal to:<BR>\n" );
document.write( "(11 * 10 * 9!) / (2! * 9!) which is equal to:<BR>\n" );
document.write( "(11 * 10) / (2 * 1) which is equal to:<BR>\n" );
document.write( "110 / 2 which is equal to 55.<BR>\n" );
document.write( "therefore:<BR>\n" );
document.write( "c(14,3) * c(11,2) is equal to 364 * 55 = 20,020.<BR>\n" );
document.write( "answers to your questions are:<BR>\n" );
document.write( "(a) How many teams made up of 3 girls and 2 boys can be selected?<BR>\n" );
document.write( "number of teams = 20,020.<BR>\n" );
document.write( "(b) How many teams can be selected with at least 3 girls?<BR>\n" );
document.write( "number of teams = 33,033.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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