document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1103433>Question 1103433</A>: <I><SPAN STYLE=\"word-break: break-all;\"> in how many ways can a research team of 5 members be formed from a group consisting of 3 chemist and 7 physicist if\r<BR>\n" );
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document.write( "a. there is no restriction in the selection?<BR>\n" );
document.write( "b. the team must include exactly 2 chemist?<BR>\n" );
document.write( "c. the team must include at most 3 physicists? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #718320 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=718320\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a.  This is 10 C 5 =252 ways<BR>\n" );
document.write( "b. 3C2*7C3, since there have to be 3 physicists.  This is 3*35=105<BR>\n" );
document.write( "c. At most 3 physicists includes the first of 105<BR>\n" );
document.write( "2 physicists and 3 chemists, which is 3C3*7C2=1*21=21 ways<BR>\n" );
document.write( "1 physicist and 4 chemists doesn't work, because there are only 3 chemists.<BR>\n" );
document.write( "therefore, 126 ways. ANSWER </SPAN>\n" );
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