document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=247120>Question 247120</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A book shelf containing 20 books of which 12 are on circuit theory and 8 are on Mathematics. If three books are taken out at random, find the probability that all the three are on the same subject. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #180328 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=180328\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 20 books.\r<BR>\n" );
document.write( "\n" );
document.write( "12 on circuit theory.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "8 on mathematics.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you pick 3 at random.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "probability that all 3 are on circuit theory would be 12/20 * 11/19 * 10/18\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "probability that all 3 are on mathematics would be 8/20 * 7/19 * 6/18\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "probability that all 3 are either on circuit theory or on mathematics would be:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(12/20 * 11/19 * 10/18) + (8/20 * 7/19 * 6/18)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you can see this with smaller numbers.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "assume 5 books total.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "3 on circuit theory<BR>\n" );
document.write( "2 on math\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you pick 2 at random.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "probability all on circuit theory is 3/5 * 2/4 = 6/20\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "probability all on math is 2/5 * 1/4 = 2/20\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "probability either all circuit theory or all math is 6/20 + 2/20 = 8/20\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let abcde be the books.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "possible permutations of 2 are:\r<BR>\n" );
document.write( "\n" );
document.write( "ab<BR>\n" );
document.write( "ac<BR>\n" );
document.write( "ad<BR>\n" );
document.write( "ae<BR>\n" );
document.write( "ba<BR>\n" );
document.write( "bc<BR>\n" );
document.write( "bd<BR>\n" );
document.write( "be<BR>\n" );
document.write( "ca<BR>\n" );
document.write( "cb<BR>\n" );
document.write( "cd<BR>\n" );
document.write( "ce<BR>\n" );
document.write( "da<BR>\n" );
document.write( "db<BR>\n" );
document.write( "dc<BR>\n" );
document.write( "de<BR>\n" );
document.write( "ea<BR>\n" );
document.write( "eb<BR>\n" );
document.write( "ec<BR>\n" );
document.write( "ed\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "assume abc are books on circuit theory\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "look for all permutations of ab or ac or bc\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that would be ab ba ac ca bc cb\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that should be 6 occurrences out of 20\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "assume de are books on math.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "look for all permutations of de\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that would be de and ed\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that should be 2 occurrences out of 20\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "total possible occurrences is 8 / 20 which is the same as derived above.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );