document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=848552>Question 848552</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are three teachers and eight students on the student council. How many ways can a committee of 4 people be chosen if there must be at least one teacher on it? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #511161 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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/cgi-bin/show-face.mpl?user=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=511161\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This can be achieved by:\r<BR>\n" );
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document.write( "(3 students, 1 teacher) (2 students, 2 teachers) (1 student, 3 teachers)\r<BR>\n" );
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document.write( "(8 choose 3)(3 choose 1) + (8 choose 2)(3 choose 2) + (8 choose 1)(3 choose 3) = 260\r<BR>\n" );
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document.write( "Alternative method. There are (11 choose 4) total ways to order. The only scenario left out is [4 students, 0 teachers] (note we cannot have 0 students, 4 teachers).\r<BR>\n" );
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document.write( "So (11 choose 4) - (8 choose 4)(3 choose 0) = 260 </SPAN>\n" );
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