document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=626167>Question 626167</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A 40-member club will elect a president and elect a vice president.  How many possible ways can a president and vice president be elected from this club/\r<BR>\n" );
document.write( "\n" );
document.write( "Suppose the 40 member club instead elects two co-presidents.  How many possible ways can co-presidents be elected from this club?\r<BR>\n" );
document.write( "\n" );
document.write( "How are these questions alike and how are they different? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #394026 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=394026\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> n = 40<BR>\n" );
document.write( "want to elect a president and vice president.<BR>\n" );
document.write( "formula is P(40,2)<BR>\n" );
document.write( "P is for permutation with n = 40 and x = 2.<BR>\n" );
document.write( "the number of possible permutation is equal to 40! / (38!) which becomes:<BR>\n" );
document.write( "40 * 39 = 1560\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "n = 40<BR>\n" );
document.write( "want to elect 2 co-presidents.<BR>\n" );
document.write( "formuls is C(40,2)<BR>\n" );
document.write( "C is for combination with n = 40 and x = 2.<BR>\n" );
document.write( "the number of possible combinations is equal to 40! / (38! * 2!) which becomes:<BR>\n" );
document.write( "40 * 39 / 2 = 1560 / 2 = 780\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the difference is in the first case order was important and in the second case order was not.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is easier to see if n = 3.<BR>\n" );
document.write( "you want to elect a president and vice president.<BR>\n" );
document.write( "the formuls now becomes P(3,2) which becomes 3! / 1! which becomes 3*2 = 6 possible ways.<BR>\n" );
document.write( "those ways are:<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "president     vice president\r\n" );
document.write( "     a             b\r\n" );
document.write( "     a             c\r\n" );
document.write( "     b             c\r\n" );
document.write( "     b             a\r\n" );
document.write( "     c             a\r\n" );
document.write( "     c             b\r\n" );
document.write( "</PRE><BR>\n" );
document.write( "order was important because candidate A could be president or vice president.<BR>\n" );
document.write( "now you want to elect 2 co-presidents.<BR>\n" );
document.write( "the formula now becomes C(3,2) which becomes 3! / (1! * 2!) becomes 3*2/2 = 3<BR>\n" );
document.write( "those ways are:<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "co-president     co-president\r\n" );
document.write( "     a               b\r\n" );
document.write( "     a               c\r\n" );
document.write( "     b               c\r\n" );
document.write( "</PRE><BR>\n" );
document.write( "order was not important here since there is no difference between a co-president and a co-president<BR>\n" );
document.write( "candidate A can be one of the candidates for co-president while candidate B can be one of the candidates for co-president - which co-president position each takes doesn't matter.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );