document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1113913>Question 1113913</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the difference between nCk and nPk </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #728960 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=728960\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> nCk is the combination formula.<BR>\n" );
document.write( "nPk is the permutation formula.\r<BR>\n" );
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document.write( "combination formula does not take order into consideration.<BR>\n" );
document.write( "permutation formula does.\r<BR>\n" );
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document.write( "combination formula is nCk = n! / (k! * (n-k)!)\r<BR>\n" );
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document.write( "permutation formula is nPk - n! / (n-k)!.\r<BR>\n" );
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document.write( "that k! in the denominator of the nCk formula is what removes consideration of order within each set.\r<BR>\n" );
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document.write( "here's a simple example:\r<BR>\n" );
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document.write( "consider the set {abcd}\r<BR>\n" );
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document.write( "n = 4<BR>\n" );
document.write( "k = 2\r<BR>\n" );
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document.write( "this means you want to get all possible sets of 2 elements each from a set of 4 elements.\r<BR>\n" );
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document.write( "4C2 = 4! / (2! * 2!) = 6\r<BR>\n" );
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document.write( "4P2 = 4! / 2! = 12\r<BR>\n" );
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document.write( "4C2 sets would be:\r<BR>\n" );
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document.write( "ab<BR>\n" );
document.write( "ac<BR>\n" );
document.write( "ad<BR>\n" );
document.write( "bc<BR>\n" );
document.write( "bd<BR>\n" );
document.write( "cd\r<BR>\n" );
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document.write( "4P2 sets would be:\r<BR>\n" );
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document.write( "ab<BR>\n" );
document.write( "ac<BR>\n" );
document.write( "ad<BR>\n" );
document.write( "bc<BR>\n" );
document.write( "bd<BR>\n" );
document.write( "cd\r<BR>\n" );
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document.write( "ba<BR>\n" );
document.write( "ca<BR>\n" );
document.write( "da<BR>\n" );
document.write( "cb<BR>\n" );
document.write( "db<BR>\n" );
document.write( "dc\r<BR>\n" );
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document.write( "the 4C2 results consider ab and ba as members of the same set, since order doesn't matter within each set.\r<BR>\n" );
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document.write( "the 4P2 results consider ab as one set and ba as another separate set, since order within the set does matter.\r<BR>\n" );
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