document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=844908>Question 844908</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A class contains 8 boys and 14 girls. Two students are to be selected as student council representatives. What is the probability both are  boys? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #508990 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=508990\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> there are 8 boys and 14 girls.<BR>\n" );
document.write( "you will be selecting 2 out of the 22 total.<BR>\n" );
document.write( "the number of ways that can occur is 22C2 = 231.<BR>\n" );
document.write( "the number of ways you can select 2 boys out of a total of 8 boys is 8C2 = 28<BR>\n" );
document.write( "the probability that you will select 2 boys is the number of ways you can select 2 boys out of 8 divided by the number of ways you can select 2 students out of 22.<BR>\n" );
document.write( "that probability would be equal to 28 / 231 = .12 rounded to  2 decimal places.\r<BR>\n" );
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document.write( "let's look at it another way.<BR>\n" );
document.write( "the probability that the first pick will be a boy is 8/22.<BR>\n" );
document.write( "the probability that the second pick will also be a boy is 7/21<BR>\n" );
document.write( "the probability that both will be a boy is 8/22 * 7/21 which is equal to 56 / 462 which is equivalent to 28 / 231.\r<BR>\n" );
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document.write( "   <BR>\n" );
document.write( "the decimal equivalent to this is .12 rounded to 2 decimal places.<BR>\n" );
document.write( "the simplest fraction will be 4/33 since both 28 and 231 are divisible by 7.\r<BR>\n" );
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document.write( "22C2 is equal to 22! / (2! * 20!)<BR>\n" );
document.write( "8C2 is equal to 8! / (2! * 6!)<BR>\n" );
document.write( "the general combination equation is:<BR>\n" );
document.write( "nCx = n! / (x! * (n-x)!)\r<BR>\n" );
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document.write( "the best way to see this is to use much smaller numbers so you can identify each possible combination.<BR>\n" );
document.write( "assume 3 boys and 2 girls and you pick a team of 2 and you want to know the probability that you will pick 2 boys.<BR>\n" );
document.write( "assuming boys are letters and girls are number, you will get the following possible combinations of 2 students.<BR>\n" );
document.write( "ab<BR>\n" );
document.write( "ac<BR>\n" );
document.write( "a1<BR>\n" );
document.write( "a2<BR>\n" );
document.write( "bc<BR>\n" );
document.write( "b1<BR>\n" );
document.write( "b2<BR>\n" );
document.write( "c1<BR>\n" );
document.write( "c2<BR>\n" );
document.write( "12<BR>\n" );
document.write( "that's a total of 10 possible combinations of 2 students.<BR>\n" );
document.write( "out of those 10 possible combinations, 3 are all boys.<BR>\n" );
document.write( "they are:<BR>\n" );
document.write( "ab<BR>\n" );
document.write( "ac<BR>\n" );
document.write( "bc<BR>\n" );
document.write( "the rest are either boy and girl or all girl.\r<BR>\n" );
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document.write( "the formulas you would use in this simplified example are:\r<BR>\n" );
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document.write( "3C2 / 5C2 which results in 3/10.<BR>\n" );
document.write( "3/5 * 2/4 which results in 6/20 which results in 3/10.\r<BR>\n" );
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document.write( "either method results in the same probability as it should.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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