document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1096884>Question 1096884</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A car dealership has 7 red, 14 silver, and 4 black cars on the lot. Ten cars are randomly chosen to be displayed in front of the dealership. <BR>\n" );
document.write( "a) Find the probability that 4 cars are red and that the rest are silver.<BR>\n" );
document.write( "b) Find the probability that 6 cars are red and 4 cars are black.<BR>\n" );
document.write( "c) Find the probability that exactly 7 cars are red.\r<BR>\n" );
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document.write( "HELP. Please answer with Full Details.\r<BR>\n" );
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document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #711298 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13206)</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=711298\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>I will assume since you are working a problem like this that you are familiar with \"n choose r\", which I will represent with C(n,r).  That number is the number of ways of choosing r of n identical objects.<br><BR>\n" );
document.write( "Overall, you are choosing 10 of the total 25 cars for the display, so the total number of possible choices (the denominator of your probability fraction) is C(25,10).<br><BR>\n" );
document.write( "For case (a), you need to choose 7 of the 7 red cars, AND 3 of the 14 silver cars, AND 0 of the 4 black cars.  As always when calculating probabilities, those \"AND\"s mean you are going to multiply the individual probabilities.  So for case (a), the numerator is [C(7,7)*C(14,3)*C(4,0)]<br><BR>\n" );
document.write( "Answer for part (a): <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28C%287%2C7%29%2AC%2814%2C3%29%2AC%284%2C0%29%29%2FC%2825%2C10%29 ALIGN=MIDDLE  ALT=\"%28C%287%2C7%29%2AC%2814%2C3%29%2AC%284%2C0%29%29%2FC%2825%2C10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "By similar analysis, the answer for part (b) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28C%287%2C6%29%2AC%2814%2C0%29%2AC%284%2C4%29%29%2FC%2825%2C10%29 ALIGN=MIDDLE  ALT=\"%28C%287%2C6%29%2AC%2814%2C0%29%2AC%284%2C4%29%29%2FC%2825%2C10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "For part (c) we need to do a bit more work.  We know all 7 red cars must be chosen (C(7,7)); but we could have either 3 silver and 0 black, OR 2 silver and 1 black, OR 1 silver and 2 black, OR 0 silver and 3 black.  And again, as always in probability those \"OR\"s mean we will be adding probabilities.<br><BR>\n" );
document.write( "So the numerator for case (c) is C(7,7) multiplied by the SUM of C(14,3)*C(4,0), C(14,2)*C(4,1), C(14,1)*C(4,2), and C(14,0)*C(4,3).<br><BR>\n" );
document.write( "Answer for part (c):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28C%287%2C7%29%2A%28C%2814%2C3%29%2AC%284%2C0%29+%2B+C%2814%2C2%29%2AC%284%2C1%29+%2B+C%2814%2C1%29%2AC%284%2C2%29+%2B+C%2814%2C0%29%2AC%284%2C3%29%29%29%2FC%2825%2C10%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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