document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1089666>Question 1089666</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In how many ways can a committee consisting of <BR>\n" );
document.write( "4<BR>\n" );
document.write( " faculty members and <BR>\n" );
document.write( "5<BR>\n" );
document.write( " students be formed if there are <BR>\n" );
document.write( "10<BR>\n" );
document.write( " faculty members and <BR>\n" );
document.write( "13<BR>\n" );
document.write( " students eligible to serve on the committee?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #704044 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=704044\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\"><BR>\n" );
document.write( "Problem: \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In how many ways can a committee consisting of 4 faculty members and 5 students be formed if there are 10 faculty members and 13 students eligible to serve on the committee?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-------------------------------------------------------<BR>\n" );
document.write( "Steps:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Use the combination formula to determine how many ways there are to pick the four faculty members (from a pool of ten)<BR>\n" );
document.write( "n C r = (n!)/(r!*(n-r)!)<BR>\n" );
document.write( "10 C 4 = (10!)/(4!*(10-4)!)<BR>\n" );
document.write( "10 C 4 = (10!)/(4!*6!)<BR>\n" );
document.write( "10 C 4 = (10*9*8*7*6!)/(4!*6!)<BR>\n" );
document.write( "10 C 4 = (10*9*8*7)/(4!)<BR>\n" );
document.write( "10 C 4 = (10*9*8*7)/(4*3*2*1)<BR>\n" );
document.write( "10 C 4 = 5040/24<BR>\n" );
document.write( "10 C 4 = 210 <BR>\n" );
document.write( "There are 210 different ways to pick the four faculty members (from a pool of ten)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Use the combination formula to determine how many ways there are to pick the five students (from a pool of thirteen)<BR>\n" );
document.write( "n C r = (n!)/(r!*(n-r)!)<BR>\n" );
document.write( "13 C 5 = (13!)/(5!*(13-5)!)<BR>\n" );
document.write( "13 C 5 = (13!)/(5!*8!)<BR>\n" );
document.write( "13 C 5 = (13*12*11*10*9*8!)/(5!*8!)<BR>\n" );
document.write( "13 C 5 = (13*12*11*10*9)/(5!)<BR>\n" );
document.write( "13 C 5 = (13*12*11*10*9)/(5*4*3*2*1)<BR>\n" );
document.write( "13 C 5 = 154440/120<BR>\n" );
document.write( "13 C 5 = 1287<BR>\n" );
document.write( "There are 1287 ways to pick the five students (from a pool of thirteen)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Multiply the two results to get 210*1287 = 270270\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-------------------------------------------------------<BR>\n" );
document.write( "Answer: <font color=red>270270</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Note: it's not a typo that \"270\" is written twice. Also, the order of any of the members doesn't matter. <BR>\n" );
document.write( "</font>  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );