document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1067726>Question 1067726</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In how many ways can a group of 4 students and a teacher be chosen from 12 students and 4 teachers? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #682859 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=682859\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you've got 12 students and 4 teachers.<BR>\n" );
document.write( "you want to choose 4 students and 1 teacher.\r<BR>\n" );
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document.write( "the students can be chosen in c(12,4) ways.<BR>\n" );
document.write( "the teacher can be chosen in c(4,1) ways.<BR>\n" );
document.write( "they can both be chosen in c(12,4) * c(4,1) ways.\r<BR>\n" );
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document.write( "c(12,4) = 12! / (4! * 8!) = 495<BR>\n" );
document.write( "c(4,1) = 4! / (1! * 3!) = 4<BR>\n" );
document.write( "495 * 4 = 1980\r<BR>\n" );
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document.write( "they can both be chosen in 1980 ways.\r<BR>\n" );
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document.write( "to see how it works, make it real simple.<BR>\n" );
document.write( "assume 3 students and 2 teacher.<BR>\n" );
document.write( "you want 2 students and 1 teacher.\r<BR>\n" );
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document.write( "per the formula, this can ocurr in c(3,2) * c(2,1) ways which is equal to 6 ways.\r<BR>\n" );
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document.write( "let the students be a,b,c<BR>\n" );
document.write( "let the teachers be 1,2\r<BR>\n" );
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document.write( "you want 2 students and 1 teacher.\r<BR>\n" );
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document.write( "the number of ways will be:\r<BR>\n" );
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document.write( "a,b,1<BR>\n" );
document.write( "a,b,2<BR>\n" );
document.write( "a,c,1<BR>\n" );
document.write( "a,c,2<BR>\n" );
document.write( "b,c,1<BR>\n" );
document.write( "b,c,2\r<BR>\n" );
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document.write( " </SPAN>\n" );
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