document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1107603>Question 1107603</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Read the question carefully.  Sample question: “80% of people who purchase pet insurance are women.  If 9 pet insurance owners are randomly selected, find the probability that exactly 6 are women.”\r<BR>\n" );
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document.write( "I am trying to have this problem broken down. Can you please explain how 84 came from 9! / (9-6)!6! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #722613 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=722613\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> p(x) = p^x * q^(n-x) * c(n,x)\r<BR>\n" );
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document.write( "p(x) is the probability of exactly occurrences.<BR>\n" );
document.write( "n = number of total occurrences.<BR>\n" );
document.write( "p = probability of success on one trial.<BR>\n" );
document.write( "q = probability of failure on one trial.<BR>\n" );
document.write( "c(n,x) = number of ways you can get a set of 8 out of a set of n.\r<BR>\n" );
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document.write( "n = 9<BR>\n" );
document.write( "x = 6<BR>\n" );
document.write( "p = .8<BR>\n" );
document.write( "q = 1 - .8 = .2<BR>\n" );
document.write( "c(9,6) = 9! / (6! * 3!) = 84\r<BR>\n" );
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document.write( "p(6) = .8^6 * .2^3 * 84 = .176160768\r<BR>\n" );
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document.write( "the sum of all probabilities must be equal to 1.\r<BR>\n" );
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document.write( "the following excel spreadsheet shows this to be true.\r<BR>\n" );
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document.write( "look below the spreadsheet for the answer to your question.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/012601.jpg\" alt=\"$$$\">\r<BR>\n" );
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document.write( " Can you please explain how 84 came from 9! / (9-6)!6!\r<BR>\n" );
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document.write( "c(n,x) = n! / (x! * (n-x)!)\r<BR>\n" );
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document.write( "in your problem, this becomes c(9,6) = 9! / (6! * (9-6)!)\r<BR>\n" );
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document.write( "simplify this to get c(9,6) = 9! / (6! * 3!)\r<BR>\n" );
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document.write( "simplify further to get c(9,6) = (9*8*7*6*5*4*3*2*1) / (6*5*4*3*2*1 * 3*2*1)\r<BR>\n" );
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document.write( "you have a block of (6*5*4*3*2*1) in the numerator and the denominator that cancels out and you are left with c(9,6) = (9*8*7) / (3*2*1)\r<BR>\n" );
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document.write( "the 3 in the denominator goes into the 9 in the numerator 3 times.<BR>\n" );
document.write( "the 2 in the denominator goes into the 8 in the numerator 4 times.\r<BR>\n" );
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document.write( "you are left with c(9,6) = 3*4*7 which is equal to 12 * 7 which is equal to 84.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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