document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1096888>Question 1096888</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Theo owns a large company and is hiring five people from an applicant pool consisting of eight men and six women. What is the probability that Theo will hire all men? Would this be unusual? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #711339 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=711339\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If Theo lists the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2B6=14 ALIGN=MIDDLE  ALT=\"8%2B6=14\"   DISABLED_style= \"max-width:90%; height:auto;\" > candidates in order of most qualified to least qualified,<BR>\n" );
document.write( "how many possible seequences could represent the first 5 names in that list?<BR>\n" );
document.write( "How many of those sequences of 5 names would only have names of men?<BR>\n" );
document.write( "There are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14%2A13%2A12%2A11%2A10 ALIGN=MIDDLE  ALT=\"14%2A13%2A12%2A11%2A10\"   DISABLED_style= \"max-width:90%; height:auto;\" > possible seequences of 5 names that can be made from the names of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14 ALIGN=MIDDLE  ALT=\"14\"   DISABLED_style= \"max-width:90%; height:auto;\" > applicants.<BR>\n" );
document.write( "There are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2A7%2A6%2A5%2A4 ALIGN=MIDDLE  ALT=\"8%2A7%2A6%2A5%2A4\"   DISABLED_style= \"max-width:90%; height:auto;\" > possible seequences of 5 names that can be made from the names of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > male applicants.<BR>\n" );
document.write( "As only <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2A7%2A6%2A5%2A4 ALIGN=MIDDLE  ALT=\"8%2A7%2A6%2A5%2A4\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14%2A13%2A12%2A11%2A10 ALIGN=MIDDLE  ALT=\"14%2A13%2A12%2A11%2A10\"   DISABLED_style= \"max-width:90%; height:auto;\" > possible sequences of 5 applicant names would use only names of men,<BR>\n" );
document.write( "random choice would make the probability that Theo hires only men<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2A7%2A6%2A5%2A4%2F%2814%2A13%2A12%2A11%2A10%29=8%2A7%2A6%2A5%2A4%2F%287%2A2%2A13%2A6%2A2%2A11%2A5%2A2%29=8%2A4%2F%282%2A13%2A2%2A11%2A2%29=2%2A2%2A2%2A4%2F%282%2A13%2A2%2A11%2A2%29=4%2F%2813%2A11%29=highlight%284%2F143%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That is about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%280.028%29 ALIGN=MIDDLE  ALT=\"highlight%280.028%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%222.8%25%22%29 ALIGN=MIDDLE  ALT=\"highlight%28%222.8%25%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "If the candidates are supposed to be similarly qualified for the jobs,<BR>\n" );
document.write( "that would be unusual.<BR>\n" );
document.write( " <BR>\n" );
document.write( "NOTES:<BR>\n" );
document.write( "A teacher may insist in figuring out number of possible sets instead of lists of candidates,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14%2A13%2A12%2A11%2A10%2F%285%2A4%2A3%2A2%29 ALIGN=MIDDLE  ALT=\"14%2A13%2A12%2A11%2A10%2F%285%2A4%2A3%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for total sets and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2A7%2A6%2A5%2A4%2F%285%2A4%2A3%2A2%29 ALIGN=MIDDLE  ALT=\"8%2A7%2A6%2A5%2A4%2F%285%2A4%2A3%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for men-only sets.<BR>\n" );
document.write( "However, common sense and math tell you that the result of the calculation would be the same.<BR>\n" );
document.write( "A teacher may want you to use the symbols, vocabulary words (such as permutations, combinations, factorials), and \"formulas\" taught in class.<BR>\n" );
document.write( "Unfortunately, symbols, words and formulas vary, so I did not throw in any.<BR>\n" );
document.write( "Besides, we need more reasoning/understanding, and less formula-memorizing. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );