document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1051667>Question 1051667</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are 8 different foods in the refrigerator. How many different ways can we take 3 of them to make a meal, if the order of the items eaten is not important? \r<BR>\n" );
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document.write( "If the order of the 3 different foods eaten is important? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #667120 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=667120\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> combination formula if order is not important.<BR>\n" );
document.write( "permutation formula if order is important.\r<BR>\n" );
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document.write( "combination formula is c(n,x) = n! / (x! * (n-x)!)\r<BR>\n" );
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document.write( "permutation formula is p(n,x) = n! / (n-x!).\r<BR>\n" );
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document.write( "n = 8<BR>\n" );
document.write( "x = 3\r<BR>\n" );
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document.write( "c(n,x) = 8! / (3! * 5!) = (8*7*6*5!) / (3*2*1*5!) = (8*7*6) / (3*2*1) = 56\r<BR>\n" );
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document.write( "p(n,x) = 8! / (5!) = (8*7*6*5!) / 5! = (8*7*6) = 336\r<BR>\n" );
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document.write( "the difference is the 3!.\r<BR>\n" );
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document.write( "when order is important, the same elements can exist in different sets, but in different order.\r<BR>\n" );
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document.write( "example:\r<BR>\n" );
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document.write( "ab is one set where order is not important.<BR>\n" );
document.write( "the elements are unique in that set but the order they are arranged in that set doesn't matter.<BR>\n" );
document.write( "it doesn't matter if they're arranged as ab or ba.<BR>\n" );
document.write( "it's still one set just as long as the elements contained in that set are in that set only.\r<BR>\n" );
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document.write( "ab and ba are two sets where order is important.<BR>\n" );
document.write( "the elements are the same in both sets but the order is different.\r<BR>\n" );
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document.write( "here are two sets where order is not important.\r<BR>\n" );
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document.write( "ab is one set and bc is another set.\r<BR>\n" );
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document.write( "they're unique because at least one of the elements in each set is different.\r<BR>\n" );
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document.write( "b is common to both sets but a is only only in the first set and c is only in the second set.\r<BR>\n" );
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document.write( "the two sets where order is not important are ab and bdc\r<BR>\n" );
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document.write( "they become 4 sets when order is important, namely ab, ba, bc, cb.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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