document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=919954>Question 919954</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A group of 2 women and 5 men decide to send a delegation to their supervisor to discuss grievances. <BR>\n" );
document.write( "If a delegation of 2 people is selected at random, determine the probability that at least 1 woman is on the delegation. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #558071 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=558071\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> there are 2 women and 5 men.\r<BR>\n" );
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document.write( "the probability that there will be at least one woman on the delegation is equal to 1 minus the probability that both people on the delegation will be men.\r<BR>\n" );
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document.write( "2 men on the delegation means no women.<BR>\n" );
document.write( "not 2 men on the delegation means at least one woman.\r<BR>\n" );
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document.write( "the probability that there will be 2 men on the delegation is equal to 5/7 * 4/6 = 20/42 which is equal to 10/21.\r<BR>\n" );
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document.write( "1 - 10/21 = 11/21\r<BR>\n" );
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document.write( "the probability that there will be at least one woman on the delegation is therefore equal to 11/21.\r<BR>\n" );
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document.write( "this can also be calculated as follows:\r<BR>\n" );
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document.write( "the number of ways you can get 2 men from 5 men without order is equal to c(5,2) which is equal to 5! / (2! * 3!) which is equal to (5*4*3!) / (2!*3!) which is equal to (5*4)/2! which is equal to 20/2 which is equal to 10.\r<BR>\n" );
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document.write( "the number of ways you can get 2 people from 7 people without order is equal to c(7,2) which is equal to 7! / (2! * 5!) which is equal to (7*6*5!) / (2!*5!) which is equal to (7*6) / 2! which is equal to 42/2 which is equal to 21.\r<BR>\n" );
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document.write( "the probability that both will be men is equal to the number of ways you can get 2 men from 5 men divided by the number of ways you can get 2 people from 7 people which is equal to 10/21.\r<BR>\n" );
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document.write( "1 minus that is equal to 11/21 which is the number of ways you can get at least 1 woman on the delegation divided by the number of ways you can get 2 people on the delegation.\r<BR>\n" );
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document.write( "if you don't get 2 men on the delegation, then at least one of the people on the delegation has to be a woman.\r<BR>\n" );
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document.write( "your solution is 11/21.\r<BR>\n" );
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document.write( "this is the probability that at least one member of the delegation will be a woman.\r<BR>\n" );
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