document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=571916>Question 571916</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You have a book collection that consists of 20 horror novels, 15 romance novels, and 25 mystery novels. You randomly pick 4 books to read during a long trip. What is the probability that you pick at least one book of each type? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #368266 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=368266\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have a book collection that consists of 20 horror novels, 15 romance novels, and 25 mystery novels. You randomly pick 4 books to read during a long trip. What is the probability that you pick at least one book of each type?<BR>\n" );
document.write( "P(at least one of each) = 1 - P(some duplicates)<BR>\n" );
document.write( "# of one-of-a-kind groups of 3 books: 20*15*25 = 7500<BR>\n" );
document.write( "# of random groups of 3 books: 60C3 = 34220<BR>\n" );
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document.write( "P(one of a kind) = 7500/34220 = 0.2192<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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