document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=717822>Question 717822</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are 9 players on a volleyball team. Only 6 players can play at one time. The players are going to pick the team randomly. How many combinations of 6 player teams can be chosen?<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 #440558 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=440558\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This problem, in mathematical terms, is: How many combinations are possible when selecting 6 out of 9. The formula for this is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%21%2F%286%21%2A3%21%29 ALIGN=MIDDLE  ALT=\"9%21%2F%286%21%2A3%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where n! is read \"n factorial\" and means 1 * 2 * 3 * ... * n<br><BR>\n" );
document.write( "Now we simplify:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2A2%2A3%2A4%2A5%2A6%2A7%2A8%2A9%29%2F%28%281%2A2%2A3%2A4%2A5%2A6%29%2A%281%2A2%2A3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cross%281%2A2%2A3%2A4%2A5%2A6%29%2A7%2A8%2A9%29%2F%28%28cross%281%2A2%2A3%2A4%2A5%2A6%29%29%2A%281%2A2%2A3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%2A8%2A9%29%2F%281%2A2%2A3%29 ALIGN=MIDDLE  ALT=\"%287%2A8%2A9%29%2F%281%2A2%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%2A4%2A2%2A3%2A3%29%2F%281%2A2%2A3%29 ALIGN=MIDDLE  ALT=\"%287%2A4%2A2%2A3%2A3%29%2F%281%2A2%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%2A4%2Across%282%29%2Across%283%29%2A3%29%2F%281%2Across%282%29%2Across%283%29%29 ALIGN=MIDDLE  ALT=\"%287%2A4%2Across%282%29%2Across%283%29%2A3%29%2F%281%2Across%282%29%2Across%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2A4%2A3%29%2F1 ALIGN=MIDDLE  ALT=\"7%2A4%2A3%29%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "84<br><BR>\n" );
document.write( "So there are 84 different groups of 6 which can be chosen from a group of 9 players. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );