document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=253039>Question 253039</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A city council consists of 7 males and 4 females. Two counsilors are selected at random to represent the city at an Elton John concert. what is the probability that\r<BR>\n" );
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document.write( "A. both councilors are male?<BR>\n" );
document.write( "B. one councilor is a male and one a female?<BR>\n" );
document.write( "C. at least one councilor is a female?\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 #185225 by </B><A HREF=/tutors/aboutme.mpl?userid=palanisamy><B>palanisamy(496)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=palanisamy><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=185225\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A city council consists of 7 males and 4 females.<BR>\n" );
document.write( "Total number of counsilors = 7+4 = 11 <BR>\n" );
document.write( "Two counsilors are selected at random <BR>\n" );
document.write( "Total number of ways of forming the committee= 11C2<BR>\n" );
document.write( "                                             = 11*10/2<BR>\n" );
document.write( "                                             =55<BR>\n" );
document.write( "A) If both counsilors are males<BR>\n" );
document.write( "  Out of 7 males 2 can be selected in 7C2 ways<BR>\n" );
document.write( "  Number of favourable events = 7*6/2 = 21<BR>\n" );
document.write( "  Probability p(A) = 21/55<BR>\n" );
document.write( "B)one councilor is a male and one a female<BR>\n" );
document.write( "  Out of 7 males 1 can be selected in 7 ways and out of 4 females 1 can be selected in 4 ways.<BR>\n" );
document.write( "  Number of favourable events = 7*4 = 28<BR>\n" );
document.write( "  Probability p(B) = 28/55<BR>\n" );
document.write( "C). At least one councilor is a female<BR>\n" );
document.write( "There are two possibilities.<BR>\n" );
document.write( "one male and one female or 2 females.<BR>\n" );
document.write( "In the first case probability = 28/55  ...(1)<BR>\n" );
document.write( "In the second case, out of 4 females 2 can be selected in 4C2 ways.<BR>\n" );
document.write( "Number of favourable events = 4*3/2 = 6<BR>\n" );
document.write( "  Probability  = 6/55                  ...(2)<BR>\n" );
document.write( "The required probability that at least one councilor <BR>\n" );
document.write( "                      is a female = (28/55)+(6/55)<BR>\n" );
document.write( "                                  = 34/55\r<BR>\n" );
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