document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=91014>Question 91014</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A total of 14 people - 8 men and 6 women have applied for admission to a business school.  The school has 5 openings.\r<BR>\n" );
document.write( "\n" );
document.write( "a.  How many ways are there of selecting the students to be admitted?<BR>\n" );
document.write( "b.  How many ways are there if at least 4 of them must be women?<BR>\n" );
document.write( "c.  How many ways are there if at least 3 of them must be women?<BR>\n" );
document.write( "d.  How many ways if exatly 3 of them must be men?<BR>\n" );
document.write( "e.  How many ways if at least one of them must be a man?\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you all for your help.  I appreciate it! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #66087 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=66087\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A total of 14 people - 8 men and 6 women have applied for admission to a business school. The school has 5 openings. <BR>\n" );
document.write( "a. How many ways are there of selecting the students to be admitted?<BR>\n" );
document.write( "14C5 = 2002 ways<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "b. How many ways are there if at least 4 of them must be women?<BR>\n" );
document.write( "# of ways if 4 women are selected and one man + # of ways if 5 women are selecte<BR>\n" );
document.write( "= 6C4*8C1 = 120 ways<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "c. How many ways are there if at least 3 of them must be women?<BR>\n" );
document.write( "6C3*8C2 + 6C4*8C1 + 6C5 = 686 ways<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "d. How many ways if exatly 3 of them must be men?<BR>\n" );
document.write( "8C3*6C2 = 840<BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "e. How many ways if at least one of them must be a man? <BR>\n" );
document.write( "Answer: 8C1*6C4 + 8C2*6C3 + 8C3*6C2 + 8C4*6C1 + 8C5 = ?<BR>\n" );
document.write( "I'll leave that to you.<BR>\n" );
document.write( "=================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );