document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=351398>Question 351398</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A parent- teacher committee consisting of 4 people is to be formed from 20 parents and 5 teachers.  Find the probability that the committee will consist of these people. (assume that the selection will be random).\r<BR>\n" );
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document.write( "a. all teachers<BR>\n" );
document.write( "b. 2 teachers and 2 parents<BR>\n" );
document.write( "c. all parents <BR>\n" );
document.write( "d. 1 teacher and 3 parents </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #251087 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=251087\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=”Garamond” size=”+2”>\r<BR>\n" );
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document.write( "The probability of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large k\"> successes in <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\"> trials where the probability of success is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large p\"> is given by:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE\ \ \ \ \ \ \ \ \ \ P_n(k,p)\ =\ \left(n\cr{k}\right)\left(p\right)^k\left(1\ -\ p\right)^{n\,-\,k}\">\r<BR>\n" );
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document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(n\cr{k}\right)\"> is the number of combinations of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\"> things taken <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large k\"> at a time and is computed using <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{n!}{k!(n\,-\,k)!\">\r<BR>\n" );
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document.write( "There are 25 people to choose from, 20 parents and 5 teachers, so the probability of picking a teacher on any given trial is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{5}{25}\ =\ 0.2\">.\r<BR>\n" );
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document.write( "For your first part you want to calculate:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE\ \ \ \ \ \ \ \ \ \ P_4(4,0.2)\ =\ \left(4\cr{4}\right)\left(0.2\right)^4\left(0.8\right)^{0}\">\r<BR>\n" );
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document.write( "For the second part:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE\ \ \ \ \ \ \ \ \ \ P_4(2,0.2)\ =\ \left(4\cr{2}\right)\left(0.2\right)^2\left(0.8\right)^{2}\">\r<BR>\n" );
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document.write( "For the third part:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE\ \ \ \ \ \ \ \ \ \ P_4(0,0.2)\ =\ \left(4\cr{0}\right)\left(0.2\right)^0\left(0.8\right)^{4}\">\r<BR>\n" );
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document.write( "For the fourth part:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE\ \ \ \ \ \ \ \ \ \ P_4(1,0.2)\ =\ \left(4\cr{1}\right)\left(0.2\right)^1\left(0.8\right)^{3}\">\r<BR>\n" );
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document.write( "Calculation hints:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(n\cr{n}\right)\ =\ \left(n\cr{0}\right)\ =\ 1\ \forall\ n\ \in\ \mathbb{N}\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x^0\ =\ 1\ \forall\ x\ \in\ \mathbb{R}\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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