document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206563>Question 1206563</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose a designer has a palette of 11 colors to work with, and wants to design a flag with 4 vertical stripes, all of different colors.\r<BR>\n" );
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document.write( "How many possible flags can be created? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844110 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=844110\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if he cares how the stripes are arranged, then the formula is p(11,4).\r<BR>\n" );
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document.write( "if he only cares about the colors and is not concerned with their position in the flag, then the formula is c(11,4).\r<BR>\n" );
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document.write( "since many flags have the same colors in different arrangement, then i would thin that p(11,4) would be more applicable.\r<BR>\n" );
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document.write( "c(11,4) = 11! / (4! * 7!) = (11 * 10 * 9 * 8) / (4 * 3 * 2 * 1) = 330\r<BR>\n" );
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document.write( "p(11,4) = 11! / (7!) = (11 * 10 * 9 * 8) = 7920\r<BR>\n" );
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document.write( "the difference between c(n,x) and p(n,x) is as follows.\r<BR>\n" );
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document.write( "suppose n = 3 and x = 2 and the 3 elements to choose from are ABC.\r<BR>\n" );
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document.write( "c(3,2) = 3! / 2! = (3 * 2 * 1) / (2 * 1) = 3.<BR>\n" );
document.write( "p(3,2) = 3! / 1! = (3 * 2) = 6\r<BR>\n" );
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document.write( "the number of combinations is 3.<BR>\n" );
document.write( "they are: AB, AC, BC<BR>\n" );
document.write( "the number of permutations is 6.<BR>\n" );
document.write( "they are: AB, BA, AC, CA, BC, CB.\r<BR>\n" );
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document.write( "with combinations, AB and BA are considered part of the same set because the order of the elements within the set is not important.\r<BR>\n" );
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document.write( "with permutations, AB and BA are considered different sets because the order of the elements within the set is important.\r<BR>\n" );
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document.write( "if two countries had the same colors and the same shape, then the only thing that would distinguish them would be the order of the colors in the flag.\r<BR>\n" );
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document.write( "i would go with the permutations number of 7920.\r<BR>\n" );
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document.write( "the possible ordering of the 4 different colors would be 4! = 4 * 3 * 2 * 1 = 24.\r<BR>\n" );
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document.write( "if you take that away, then you get the number of combinations because 7920 / 24 = 330.<BR>\n" );
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