document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=233437>Question 233437</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 16)  In how many ways can  7 people be chosen and arranged in a straight line, if there are  9 people from whom to choose? 							16)   ______ <BR>\n" );
document.write( "A) 72 ways 		B)  63 ways <BR>\n" );
document.write( "C) 144 ways 		D)  181,440 ways <BR>\n" );
document.write( " *****AM I USING PERMUTATION, COMBINATIONS or is it 9*7=63?******<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #172295 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=172295\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If where in the line they are placed is important, then you are dealing with permutations.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If where in the line they are placed is not important, then you are dealing with combinations.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Example:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "choose 2 out of 3 people.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "people are abc.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If order is important, then you can choose ...\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "ab<BR>\n" );
document.write( "ac<BR>\n" );
document.write( "bc<BR>\n" );
document.write( "ba<BR>\n" );
document.write( "ca<BR>\n" );
document.write( "cb\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "= 6 ways\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If order is not important, then you can choose ...\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( "= 3 ways\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If permutations, the answer would be n! / (n-x)! where n is the total number to choose from and x is the amount you want to draw from that population.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "n = 3, x = 2, permutations = 3! / 1! = 3*2*1/1 = 6\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If combinations, the answer would be n! / ((n-x)! * x!)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "n = 3, x = 2, combinations = 3! / (1! * 2!) = 3*2*1/1*2*1 = 3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In your problem, the numbers come out as follows:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Permutations = 9! / (9-7)! = 9! / 2! = 9*7*6*5*4*3*2*1/2*1 = 181440.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Combinations = 9! / (2!*7!) = 9*8*7! /2!*7! = 9*8/2*1 = 72/2 = 36\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since 36 is not one of the answers, I would assume permutations and select D.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If it was just combination, they would have said:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "16)  In how many ways can  7 people be chosen if there are 9 people from whom to choose? \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The question was posede as:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "16)  In how many ways can  7 people be chosen and arranged in a straight line, if there are  9 people from whom to choose? \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The word arranged should have been your permutation clue.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "That's what I think, anyway.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );