document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=89823>Question 89823</A>: <I><SPAN STYLE=\"word-break: break-all;\"> there are 12 trumpet players in the marching band, but there is only room for 3 of them in the jazz band. how many diffrent combinations of trumpet players could be selected for the jazz band out of the 12?<BR>\n" );
document.write( "a. 1728<BR>\n" );
document.write( "b. 36<BR>\n" );
document.write( "c. 1320<BR>\n" );
document.write( "d. 220 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #65211 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=65211\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Since order does not matter, we can use the <a  rel=nofollow HREF=http://www.mathwords.com/c/combination_formula.htm>combination formula</a>:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{n}C_{r}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%21%2F%28n-r%29%21r%21 ALIGN=MIDDLE  ALT=\"n%21%2F%28n-r%29%21r%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given formula\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{12}C_{3}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%21%2F%2812-3%29%213%21 ALIGN=MIDDLE  ALT=\"12%21%2F%2812-3%29%213%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=12 ALIGN=MIDDLE  ALT=\"n=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=3 ALIGN=MIDDLE  ALT=\"r=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{12}C_{3}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%21%2F9%213%21 ALIGN=MIDDLE  ALT=\"12%21%2F9%213%21\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12-3 ALIGN=MIDDLE  ALT=\"12-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 9\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Expand 12!<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{12}C_{3}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F9%213%21 ALIGN=MIDDLE  ALT=\"%2812%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F9%213%21\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Expand 9!<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{12}C_{3}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F%289%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%293%21 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{12}C_{3}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%2A11%2A10%2Across%289%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%29%2F%28cross%289%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%293%21 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >  Cancel\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{12}C_{3}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%2A11%2A10%29%2F3%21 ALIGN=MIDDLE  ALT=\"%2812%2A11%2A10%29%2F3%21\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Simplify\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Expand 3!<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{12}C_{3}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%2A11%2A10%29%2F%283%2A2%2A1%29 ALIGN=MIDDLE  ALT=\"%2812%2A11%2A10%29%2F%283%2A2%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{12}C_{3}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1320%2F%283%2A2%2A1%29 ALIGN=MIDDLE  ALT=\"1320%2F%283%2A2%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Multiply 12*11*10 to get 1,320\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{12}C_{3}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1320%2F6 ALIGN=MIDDLE  ALT=\"1320%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 3*2*1 to get 6\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{_{12}C_{3}=\"><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=220 ALIGN=MIDDLE  ALT=\"220\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now divide\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So 12 choose 3 (where order doesn't matter) yields 220 unique combinations\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the answer is d) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );