document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=565269>Question 565269</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A production facility employs 20 workers on the day shift, 15 workers on the swing shift, and 10<BR>\n" );
document.write( "workers on the graveyard shift. A quality control consultant is to select 6 of these workers for in<BR>\n" );
document.write( "depth interviews. Suppose the selection is made in such a way that any particular group of 6<BR>\n" );
document.write( "workers has the same chance of being selected as does any other group (drawing 6 slips without<BR>\n" );
document.write( "replacement from among 45). What is the probability that at least two different shifts will be<BR>\n" );
document.write( "represented among the selected workers? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #365819 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=365819\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A production facility employs 20 workers on the day shift, 15 workers on the swing shift, and 10<BR>\n" );
document.write( "workers on the graveyard shift. A quality control consultant is to select 6 of these workers for in<BR>\n" );
document.write( "depth interviews. Suppose the selection is made in such a way that any particular group of 6<BR>\n" );
document.write( "workers has the same chance of being selected as does any other group (drawing 6 slips without<BR>\n" );
document.write( "replacement from among 45). What is the probability that at least two different shifts will be<BR>\n" );
document.write( "represented among the selected workers?<BR>\n" );
document.write( "---<BR>\n" );
document.write( "P(at least 2 shifts) = 1 - P(1 shift represented)<BR>\n" );
document.write( "= 1 - [20C6 + 15C6 + 10C6]/45C6 <BR>\n" );
document.write( "----<BR>\n" );
document.write( "= 1 - [43975/8145060]<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "= 0.9946<BR>\n" );
document.write( "=============<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );