document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192754>Question 1192754</A>: <I><SPAN STYLE=\"word-break: break-all;\">  A team of five is to be chosen from four men and five women to work on a special project<BR>\n" );
document.write( " i. In how many ways can the team be chosen?<BR>\n" );
document.write( " ii. In how many ways can the team be chosen to include just three women?<BR>\n" );
document.write( " iii. What is the probability that the team just includes three women?<BR>\n" );
document.write( " iv. What is the probability that the team include at least three women? <BR>\n" );
document.write( "v. What is the probability that the team includes more men than women<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 #824698 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=824698\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 9C5 ways to choose the groups=126 ways<BR>\n" );
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document.write( "ii. numerator its 5C3*4C2 for 3 women and therefore 2 men=60, so there are 60 ways<BR>\n" );
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document.write( "iii probability is 60/126 or 10/21.<BR>\n" );
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document.write( "iv. at least 3 women includes 3,4,5. We know 60 ways for 3. For 4 it is 5C4*4C1=20 ways and for 5 women there is only one way. Therefore , there is 81/126 probability or 9/14.<BR>\n" );
document.write( "v.Look at 2 women this has 5C2*4C3=40 ways<BR>\n" );
document.write( "For 1 woman 4C4*5C1=5 ways.<BR>\n" );
document.write( "Can't be 0 women.<BR>\n" );
document.write( "1woman-4 men=5 ways<BR>\n" );
document.write( "2W 3M-40 ways<BR>\n" );
document.write( "3W2M-60 ways<BR>\n" );
document.write( "4W1M-20 ways<BR>\n" );
document.write( "5W0M-1 way<BR>\n" );
document.write( "They add up to 126. They have to.<BR>\n" );
document.write( "More men then women occurs 4/1 (5 ways) 3/2 (40 ways) no other ways. so probability is 45/126=15/34\r<BR>\n" );
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