document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=995781>Question 995781</A>: <I><SPAN STYLE=\"word-break: break-all;\">  I need a guidance as to how to solve this problem.\r<BR>\n" );
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document.write( " Fifteen people are summoned to jury duty. 9 are women and 6 are men.    <BR>\n" );
document.write( "(a)  In how many ways can 12 jurists be randomly selected out of the 15 people?   Show work.    <BR>\n" );
document.write( "(b)  In how many ways can 12 jurists be chosen, if 7 must be women and 5 must be men? Show work.   <BR>\n" );
document.write( "(c)  If 12 jurists are randomly selected from the 15 people, what is the probability that 5 are men and 7 are women?  Round answer to nearest ten-thousandth (4 places after decimal).  Show work. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #614462 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52818)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=614462\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( " I need a guidance as to how to solve this problem. <BR>\n" );
document.write( "Fifteen people are summoned to jury duty. 9 are women and 6 are men. <BR>\n" );
document.write( "(a) In how many ways can 12 jurists be randomly selected out of the 15 people? Show work. <BR>\n" );
document.write( "(b) In how many ways can 12 jurists be chosen, if 7 must be women and 5 must be men? Show work. <BR>\n" );
document.write( "(c) If 12 jurists are randomly selected from the 15 people, what is the probability that 5 are men and 7 are women? Round answer to nearest ten-thousandth (4 places after decimal). Show work.<BR>\n" );
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document.write( "(a) &nbsp;In how many ways can &nbsp;12&nbsp; jurists be randomly selected out of &nbsp;15&nbsp; people?\r<BR>\n" );
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document.write( "It is the standard conception of <U>combinations</U>. &nbsp;Do you know it? &nbsp;Are you familiar with it? &nbsp;If not, &nbsp;look in the lesson &nbsp;<A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Permutations/Introduction-to-Combinations-.lesson>Introduction to Combinations</A>&nbsp; in this site. \r<BR>\n" );
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document.write( "The number in which &nbsp;12&nbsp; jurists can be randomly selected out of &nbsp;15&nbsp; people is the number of combinations of &nbsp;15&nbsp; things taken &nbsp;12&nbsp; at time: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B15%5D%5E12 ALIGN=MIDDLE  ALT=\"C%5B15%5D%5E12\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%21%2F%2812%21%2A3%21%29 ALIGN=MIDDLE  ALT=\"15%21%2F%2812%21%2A3%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815%2A14%2A13%29%2F%281%2A2%2A3%29 ALIGN=MIDDLE  ALT=\"%2815%2A14%2A13%29%2F%281%2A2%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 5*7*13 = 455.\r<BR>\n" );
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document.write( "(b) &nbsp;In how many ways can &nbsp;12&nbsp; jurists be chosen, if &nbsp;7&nbsp; must be women and &nbsp;5&nbsp; must be men?\r<BR>\n" );
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document.write( "7&nbsp; jurists out of &nbsp;9&nbsp; women can be randomly chosen in &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B9%5D%5E7 ALIGN=MIDDLE  ALT=\"C%5B9%5D%5E7\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%21%2F%287%21%2A2%21%29 ALIGN=MIDDLE  ALT=\"9%21%2F%287%21%2A2%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%2A8%29%2F%281%2A2%29 ALIGN=MIDDLE  ALT=\"%289%2A8%29%2F%281%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 9*4 = 36 ways. \r<BR>\n" );
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document.write( "5&nbsp; jurists out of &nbsp;6&nbsp; men can be randomly chosen in &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B6%5D%5E5 ALIGN=MIDDLE  ALT=\"C%5B6%5D%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%21%2F%285%21%2A1%21%29 ALIGN=MIDDLE  ALT=\"6%21%2F%285%21%2A1%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F1 ALIGN=MIDDLE  ALT=\"6%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 6 ways. \r<BR>\n" );
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document.write( "Combining &nbsp;36&nbsp; ways for women with &nbsp;6&nbsp; ways for men &nbsp;(they are independent!) &nbsp;you obtain &nbsp;36*6 = 216 ways.\r<BR>\n" );
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document.write( "(c) If 12 jurists are randomly selected from the 15 people, what is the probability that 5 are men and 7 are women? \r<BR>\n" );
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document.write( "Round answer to nearest ten-thousandth (4 places after decimal).\r<BR>\n" );
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document.write( "This probability is the ratio of that two numbers we obtained as answers to problems (a) and (b): \r<BR>\n" );
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document.write( "Probability = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=216%2F455 ALIGN=MIDDLE  ALT=\"216%2F455\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.4747 (approx.)\r<BR>\n" );
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