document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197366>Question 1197366</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A committee of 4 people is to be formed from a pool of 8 people. What is the probability James is in the<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #830591 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=830591\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
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document.write( "    P = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B7%5D%5E3%2FC%5B8%5D%5E4 ALIGN=MIDDLE  ALT=\"C%5B7%5D%5E3%2FC%5B8%5D%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35%2F70 ALIGN=MIDDLE  ALT=\"35%2F70\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.5 = 50%.    <U>ANSWER</U>\r\n" );
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document.write( "The denominator is the number of all different possible quadruples of 8.\r<BR>\n" );
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document.write( "The numerator is the number of all such quadruples containing James.\r<BR>\n" );
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document.write( "Solved and explained.\r<BR>\n" );
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document.write( "This problem assumes that you are familiar with &nbsp;COMBINATIONS - - - this knowledge is a pre-requisite.\r<BR>\n" );
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document.write( "On &nbsp;Combinations, &nbsp;see introductory lessons\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Permutations/Introduction-to-Combinations-.lesson>Introduction to Combinations</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Permutations/PROOF-of-the-formula-on-the-number-of-combinations.lesson>PROOF of the formula on the number of Combinations</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Permutations/Problems-on-Combinations.lesson>Problems on Combinations</A>\r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( "Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.\r<BR>\n" );
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document.write( "The referred lessons are the part of this online textbook under the topic &nbsp;\"<U>Combinatorics: Combinations and permutations</U>\". \r<BR>\n" );
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document.write( "Save the link to this textbook together with its description\r<BR>\n" );
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document.write( "Free of charge online textbook in ALGEBRA-II<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r<BR>\n" );
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document.write( "into your archive and use when it is needed.\r<BR>\n" );
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document.write( "Sometimes, when I explain such solutions to students, I calculate the number of combinations manually,\r<BR>\n" );
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document.write( "using and showing explicit formulas.\r<BR>\n" );
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document.write( "But had I do it this way every time, &nbsp;I, &nbsp;probably, &nbsp;would lose my mind.\r<BR>\n" );
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document.write( "Therefore, &nbsp;often &nbsp;I &nbsp;use &nbsp;MS &nbsp;Excel software in my computer writing\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=combin(N,n), &nbsp;when &nbsp;I &nbsp;need the value  &nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5BN%5D%5En ALIGN=MIDDLE  ALT=\"C%5BN%5D%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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