document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=388108>Question 388108</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are 6 boys and 4 girls and a group of 5 people must be formed. How many groups are possible consisting of 2 girls and 3 boys\r<BR>\n" );
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document.write( "Answer:<BR>\n" );
document.write( "nCr=combination of n things taken r at a time= n!/((n-r)!*r!)<BR>\n" );
document.write( "4C2 * 6C3<BR>\n" );
document.write( "=6*20<BR>\n" );
document.write( "=120 groups\r<BR>\n" );
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document.write( "If a group is chosen randomly from the 10 people, find the probability that the group will consist exactly of 2 girls and 3 boys.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #274440 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=274440\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The probability that a group of 5 chosen out of a group of 10 will contain exactly 2 girls and 3 boys is equal to:<BR>\n" );
document.write( "(C(6,3) * C(4,2)) / C(10,5)\r<BR>\n" );
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document.write( "That becomes 120 / 252 = .476190476\r<BR>\n" );
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document.write( "That is the number of ways you can get a group of 5 consisting of 2 girls and 3 boys divided by the total number of ways you can get a group of 5.\r<BR>\n" );
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document.write( "It can also be calculated another way.\r<BR>\n" );
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document.write( "The probability of getting bbbgg (3 boys picked first and then 2 girls) would be:\r<BR>\n" );
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document.write( "6/10 * 5/9 * 4/8 * 4/7 * 3/6\r<BR>\n" );
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document.write( "This becomes .0476190476\r<BR>\n" );
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document.write( "You then need to multiply that by the number of different ways the group of 5 can be chosen.\r<BR>\n" );
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document.write( "That would be C(5,2) = 10\r<BR>\n" );
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document.write( "The total probability is therefore .0476190476 * 10 = .476190476\r<BR>\n" );
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document.write( "The number of ways the group of 5 can be choen is shown below:\r<BR>\n" );
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document.write( "bbbgg<BR>\n" );
document.write( "bbgbg<BR>\n" );
document.write( "bbggb<BR>\n" );
document.write( "bgbbg<BR>\n" );
document.write( "bgbgb<BR>\n" );
document.write( "bggbb<BR>\n" );
document.write( "gbbbg<BR>\n" );
document.write( "gbbgb<BR>\n" );
document.write( "gbgbb<BR>\n" );
document.write( "ggbbb\r<BR>\n" );
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document.write( "bbbgg means boy drawn first and second and third girl drawn fourth and fifth.<BR>\n" );
document.write( "bbgbg means boy drawn first and second girl drawn third boy drawn fourth girl drawn fifth.<BR>\n" );
document.write( "etc. until you get to:<BR>\n" );
document.write( "ggbbb means girls drawn first and second boy drawn third fourth and fifth.\r<BR>\n" );
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document.write( "both ways will get you the same answer.\r<BR>\n" );
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