document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1019208>Question 1019208</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use formula for Permutations to calculate in how many ways you can select 2 people out of 10, order of selection makes a difference. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #635208 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=635208\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> p(n,x) = n! / (n-x)!\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "n = 10<BR>\n" );
document.write( "x = 2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "p(n,x) becomes p(10,2) = 10! / (10-2)! = 10! / 8! = (10 * 9 * 8!) / 8!.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the 8! in the numerator and denominator cancel out and you are left with:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "p(10,2) = 10 * 9 = 90\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in the permutation formula, order makes a difference, so sets with the same elements but in different order are counted as separate sets.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in the combination formula, order does not make a difference, so sets with the same elements are only counted.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this can be seen easily when dealing with a smaller number of permutations and combinations.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "assume n = 3 and x = 2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "permutation formula ia p(n,x) = n! / (n-x)!\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "combination formula is c(n,x) = n! / (x! * (n-x)!)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that extra division by x! in the combinattion formula takes away the multiple ordered versions of the same set.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "p(3,2) = 3! / 1! = 3*2 = 6\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "c(3,2) = 3! / (2! * 1!) = (3*2)/2 = 3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "assume the elements are a, b, and c.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the number of permutations of 2 out of the 3 elements are detailed below:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "ab<BR>\n" );
document.write( "ba<BR>\n" );
document.write( "ab<BR>\n" );
document.write( "ca<BR>\n" );
document.write( "bc<BR>\n" );
document.write( "cb\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "even though ab and ba have the same elements, they are in a different order and counted separately.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the number of combinations of 2 out of the 3 elements are detailed below:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "ab<BR>\n" );
document.write( "ac<BR>\n" );
document.write( "bc\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "ba and ca and cb are not counted as separate sets because they are the same elements shown above but in a different order.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );