document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208918>Question 1208918</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A history class is comprised of 5<BR>\n" );
document.write( "female and<BR>\n" );
document.write( "9 male students. If the instructor of the class randomly chooses<BR>\n" );
document.write( "8 students from the class for an oral exam, what is the probability that<BR>\n" );
document.write( "3 female students and<BR>\n" );
document.write( "5 male students will be selected? Round your answer to<BR>\n" );
document.write( "decimal places </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #847442 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=847442\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answer: <font color=red>0.41958 approximately</font><BR>\n" );
document.write( "The exact value as a fraction is 60/143.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Explanation\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's see how many ways there are to select the girls.<BR>\n" );
document.write( "The teacher has 5 choices for the 1st slot, then 4 for the next, and 3 for the last.<BR>\n" );
document.write( "5*4*3 = 60 permutations of girls if order mattered.<BR>\n" );
document.write( "I'll assume that order doesn't matter, so we divide by 3! = 3*2*1 = 6 because this is the number of ways to arrange any trio of people. <ol><li>ABC</li><li>ACB</li><li>BAC</li><li>BCA</li><li>CAB</li><li>CBA</li></ol>Therefore the teacher has 60/6 = 10 different ways to pick the girls sub-group where order doesn't matter.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Another way to get to this result (10) is to use the nCr combination formula with n = 5 and r = 3.<BR>\n" );
document.write( "That formula is<BR>\n" );
document.write( "n C r = (n!)/(r!(n-r)!)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "There are many calculators that will quickly calculate nCr values. <BR>\n" );
document.write( "You can use this combinatorics calculator<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://www.mathsisfun.com/combinatorics/combinations-permutations-calculator.html\">https://www.mathsisfun.com/combinatorics/combinations-permutations-calculator.html</a><BR>\n" );
document.write( "to not only calculate the nCr value but also list out the possible combos. <BR>\n" );
document.write( "Refer to the \"list them\" section.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Another way to compute the nCr value is to use Pascal's Triangle. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Use any method you prefer to find that:<BR>\n" );
document.write( "There are 9C5 = 126 ways to select the boys.<BR>\n" );
document.write( "There are 14C8 = 3003 ways to pick the group of eight people regardless of gender.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Side note: <BR>\n" );
document.write( "Notation like 14C8 is equivalent to writing C(14,8)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So we found there are 10 ways to pick the girls and 126 ways to pick the boys. <BR>\n" );
document.write( "What do we do with these numbers?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Imagine we had a table that is 10 columns across and 126 rows tall.<BR>\n" );
document.write( "Of course such a massive table is a thought exercise only and not something to actually draw out on paper.<BR>\n" );
document.write( "This table has 10*126 = 1260 inner cells. <BR>\n" );
document.write( "Each inner cell represents a different combo of 3 girls and 5 boys. <BR>\n" );
document.write( "It might help to make a much smaller scaled down version of this table so you can see what I'm talking about. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Anyways the punchline of that previous paragraph is that we have 1260 different combos of three girls + five guys out of 3003 different possibilities.<BR>\n" );
document.write( "1260/3003 = 60/143 = <font color=red>0.41958 approximately</font>.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This is somewhat close to 42%\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Your instructions mention \"Round your answer to ____ decimal places\" but the value in the blank is missing. It appears to be a strange error of some kind. <BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );