document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200584>Question 1200584</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Each of the teams in a mixed volleyball league consists of 5 men and 5 women. There are 9 men and 10 women, including Julia, who are trying out for a team. How many possible teams would include Julia?<BR>\n" );
document.write( "15,876<BR>\n" );
document.write( "31,752<BR>\n" );
document.write( "45,722,880<BR>\n" );
document.write( "457,228,800 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #834751 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=834751\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "There are 9 men and 5 spots for them.<BR>\n" );
document.write( "Order does not matter.<BR>\n" );
document.write( "n = 9<BR>\n" );
document.write( "r = 5<BR>\n" );
document.write( "We use the nCr combination formula.<BR>\n" );
document.write( "n C r = (n!)/(r!(n-r)!)<BR>\n" );
document.write( "9 C 5 = (9!)/(5!*(9-5)!)<BR>\n" );
document.write( "9 C 5 = (9!)/(5!*4!)<BR>\n" );
document.write( "9 C 5 = (9*8*7*6*5!)/(5!*4!)<BR>\n" );
document.write( "9 C 5 = (9*8*7*6)/(4!)<BR>\n" );
document.write( "9 C 5 = (9*8*7*6)/(4*3*2*1)<BR>\n" );
document.write( "9 C 5 = (3024)/(24)<BR>\n" );
document.write( "9 C 5 = 126<BR>\n" );
document.write( "There are 126 ways to select the five men from a pool of nine male candidates.\r<BR>\n" );
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document.write( "Because Julia is on the team, there are 10-1 = 9 women left to pick from and 5-1 = 4 female roster spots.<BR>\n" );
document.write( "n = 9<BR>\n" );
document.write( "r = 4<BR>\n" );
document.write( "n C r = (n!)/(r!(n-r)!)<BR>\n" );
document.write( "9 C 4 = (9!)/(4!*(9-4)!)<BR>\n" );
document.write( "9 C 4 = (9!)/(4!*5!)<BR>\n" );
document.write( "9 C 4 = (9*8*7*6*5!)/(4!*5!)<BR>\n" );
document.write( "9 C 4 = (9*8*7*6)/(4!)<BR>\n" );
document.write( "9 C 4 = (9*8*7*6)/(4*3*2*1)<BR>\n" );
document.write( "9 C 4 = (3024)/(24)<BR>\n" );
document.write( "9 C 4 = 126<BR>\n" );
document.write( "There are 126 ways to select the remaining four female roster spots from a pool of nine remaining female candidates.\r<BR>\n" );
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document.write( "Side note: You can use Pascal's Triangle to determine the result of 126 calculated earlier. Look at the row that has 1,9,... and look at the 5th and 6th slots.\r<BR>\n" );
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document.write( "We found that there are...<ul><li>126 ways to pick the men</li><li>126 ways to pick the women, where Julia is on the team.</li></ul>That will give 126*126 = <font color=red>15876</font> different teams where Julia is guaranteed to be on it.\r<BR>\n" );
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document.write( "Here is a calculator that computes nCr values<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.calculatorsoup.com/calculators/discretemathematics/combinations.php\">https://www.calculatorsoup.com/calculators/discretemathematics/combinations.php</a>\r<BR>\n" );
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document.write( "Answer: <font color=red>15876</font> (choice A)<BR>\n" );
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