document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1075774>Question 1075774</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Three hundred people apply for three jobs. Sixty of the applicants are women.<BR>\n" );
document.write( "(a) If three people are selected at random, what is the probability that all are women? (Round your answer to six decimal places.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #690471 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=690471\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the probability that the first applicant will be a woman is 60/300.\r<BR>\n" );
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document.write( "assuming the first is a woman, then the probability that the second will be a woman is 59/299.\r<BR>\n" );
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document.write( "assuming the second is a woman, then the probability that the third will be a woman is 58/298.\r<BR>\n" );
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document.write( "the probability that they will all be women is therefore 60/300 * 59/299 * 58/298.\r<BR>\n" );
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document.write( "this becomes equal to .0076810846\r<BR>\n" );
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document.write( "alternately this can be viewed as the number of ways you can get 3 women out of 60 divided by the number of ways you can get 3 people out of 300.\r<BR>\n" );
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document.write( "that would be c(60,3) / c(300,3) = .0076810846.\r<BR>\n" );
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document.write( "c(60,3) = 60! / (3! * 57!)\r<BR>\n" );
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document.write( "c(300,3) = 300! / (3! * 297!)\r<BR>\n" );
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document.write( "in general, c(n,x) = n! / (x! * (n-x)!)\r<BR>\n" );
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document.write( "the calculator i used is the ti-84 plus.\r<BR>\n" );
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document.write( "it can do c(300,3) but it can't do 300! / (3! * 297!).\r<BR>\n" );
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document.write( "for whatever the reasons, the combination formula works but the equivalent factorial formula doesn't work.\r<BR>\n" );
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document.write( "it has to do with internal storage requirements in the calculator.\r<BR>\n" );
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document.write( "300! is just too large for it to handle.\r<BR>\n" );
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document.write( "i used excel as well but that can't handle it either.\r<BR>\n" );
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document.write( "surprisingly, both excel and the ti-84 could handle c(300,3).\r<BR>\n" );
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document.write( "bottom line is the results are accurate but if you try to duplicate c(300,3) by using the equivalent formula of 300! / (3! * 297!) you will have difficulty.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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