document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=246505>Question 246505</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Arrange 15 different books onto bookshelf with 3 shelves. what is the probability that the top shelf has three books under the condition that exactly one shelf is empty?\r<BR>\n" );
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document.write( "I'm don't know how to use the condition. Any help? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #180055 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=180055\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Arrange 15 different books onto bookshelf with 3 shelves. what is the probability that the top shelf has three books under the condition that exactly one shelf is empty? <BR>\n" );
document.write( "I don't know how to use the condition. Any help?<BR>\n" );
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document.write( "P(A | B) = P(A and B)/P(B)<BR>\n" );
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document.write( "P(3 on top | 1 empty) = P(3 on top AND one empty)/P(1 empty)<BR>\n" );
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document.write( "# of ways to get 3 on top: 15C3<BR>\n" );
document.write( "# of ways to pick one empty: 2<BR>\n" );
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document.write( "# of ways to pick 3 on top AND one empty = 2*15C3<BR>\n" );
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document.write( "# of ways to Place 3 without restriction: 15!<BR>\n" );
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document.write( "P(1 empty) = 2/3<BR>\n" );
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document.write( "P(3 on top | 1 empty) = (2*15C3/15!)/(2/3) = 4.639x10^-10<BR>\n" );
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document.write( "Check this out carefully.  I am not fully satisfied with it.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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