document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1103356>Question 1103356</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 6 freshmen, 8 sophomores, 10 juniors, and 9 seniors are eligible to be on a committee. If a committee of 14 students is chosen at random, what is the probability that it is made up of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors? \r<BR>\n" );
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document.write( "Even if you don't use the exact problem, it's fine, since I want to learn how to find the probability. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #718043 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=718043\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Okay; I will use different numbers: 4 freshmen, 3 sophomores, 7 juniors, and 7 seniors.  And we will still make a committee of 14 with 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors.<br><BR>\n" );
document.write( "The basic definition of probability says that the answer is<BR>\n" );
document.write( "(number of ways of choosing 2 of the 4 freshmen AND 3 of the 3 sophomores AND 4 of the 7 juniors AND 5 of the 7 seniors) divided by (the total number of ways of choosing 14 of the total 21 students).<br><BR>\n" );
document.write( "Because the calculations involve choosing among candidates, you will be using the \"n choose r\" concept repeatedly.  Since you are asking this question, I will assume you are familiar with that concept.<br><BR>\n" );
document.write( "The denominator of our probability fraction is the number of ways of choosing 14 of the 21 students: C(21,14).<br><BR>\n" );
document.write( "For the numerator, we have to choose certain numbers of each of the four class levels.  So the numerator of the probability fraction will be C(4,2)*C(3,3)*C(7,4)*C(7,5).<br><BR>\n" );
document.write( "C(21,14) = 116280; C(4,2)*C(3,3)*C(7,4)*C(7,5) = 6*1*35*21 = 4410; the probability that the committee has 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4410%2F116280+=+.0379 ALIGN=MIDDLE  ALT=\"4410%2F116280+=+.0379\"   DISABLED_style= \"max-width:90%; height:auto;\" > to 4 decimal places.<br><BR>\n" );
document.write( "Obviously the process for solving your example will be the same, just with different numbers. </SPAN>\n" );
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