document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1134734>Question 1134734</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simple random  sampling  uses a  sample of size n from a population  of size N to obtain  data  that  can  be  used  to  make  inferences  about  the  characteristics  of a population. Suppose that, from  a  population  of  50 bank  accounts, we want to take  a  random  sample  of  four  accounts in order  to  learn  about  the  population. How many  different random  samples  of  four  accounts  are possible?<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 #752216 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=752216\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> c(50,4) = 230,300\r<BR>\n" );
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document.write( "the formula used is the combination formula of c(n,x)\r<BR>\n" );
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document.write( "n is the size of the group that is being drawn from.<BR>\n" );
document.write( "x is the size of the group that is being drawn.\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( "c(50,4) = 50! / (4! * 46!)\r<BR>\n" );
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document.write( "this is equivalent to (50 * 49 * 48 * 47 * 46!) / (4! * 46!)\r<BR>\n" );
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document.write( "the 46! in the numerator and denominator cancel out and you are left with:\r<BR>\n" );
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document.write( "(50 * 49 * 48 * 47) / (4 * 3 * 2 * 1)\r<BR>\n" );
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document.write( "evaluate this to get 230,300.\r<BR>\n" );
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document.write( "each set of 4 accounts will be different from any other set of 4 accounts.\r<BR>\n" );
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document.write( "a much simpler example that can show you what i mean would be 2 accounts taken from 4 accounts.\r<BR>\n" );
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document.write( "the number of possible accounts in that case will be c(4,2) = 4! / (2! * 2!) = (4 * 3 * 2 * 1) / (2 * 1 * 2 * 1) = 6.\r<BR>\n" );
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document.write( "if the 4 accounts are a, b, c, and d, then the possible sets of 2 accounts will be:\r<BR>\n" );
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document.write( "a,b<BR>\n" );
document.write( "a,c<BR>\n" );
document.write( "a,d<BR>\n" );
document.write( "b,c<BR>\n" );
document.write( "b,d<BR>\n" );
document.write( "c,d\r<BR>\n" );
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document.write( "each set of 2 will have at least 1 member that will not be in any other set of 2.\r<BR>\n" );
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document.write( "for example, there are no other sets that have a,b in them.\r<BR>\n" );
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document.write( "the other sets can have a, and they can have b, but they will not have a,b.\r<BR>\n" );
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document.write( "this makes each set a unique combination of members.\r<BR>\n" );
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document.write( "this formula works for all size sets, only it's way too difficult to show you all the possible combinations.\r<BR>\n" );
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document.write( "something like that would best be done by computer.\r<BR>\n" );
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