document.write( "Question 1114136: In how many ways 7 different books can be arranged on a shelf? In how man many ways will a specified book be (I) at the centre? (II)
\n" );
document.write( "at either end? \n" );
document.write( "
Algebra.Com's Answer #729137 by ikleyn(52778)![]() ![]() You can put this solution on YOUR website! . \n" ); document.write( " \r\n" ); document.write( "(I) It is VERY STANDARD introductory problem on PERMUTATIONS for beginners.\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( " The answer is 7! = 1*2*3*4*5*6*7.\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( " The standard solution (=mantra) is this:\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( " You can put any of the 7 books in the 1-st position in 7 ways.\r\n" ); document.write( "\r\n" ); document.write( " You can put any of the remaining 6 books in the 2-nd position in 6 ways.\r\n" ); document.write( " \r\n" ); document.write( " You can put any of the remaining 5 books in the 3-rd position in 5 ways.\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( " . . . and so on . . . \r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( " You can put any of the remaining 2 books in the 6-th position in 2 ways.\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( " Finally, you can put the last remaining 1 book in the 7-th position in 1 way only (there is nothing to select from at this step . . . ).\r\n" ); document.write( "\r\n" ); document.write( " \r\n" ); document.write( " Since these selections/options are independent, you have 7! = 7*6*5*4*3*2*1 ways, in all.\r\n" ); document.write( "\r \n" ); document.write( "\n" ); document.write( "Solved.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "----------------- \n" ); document.write( "On Permutations, see the lessons\r \n" ); document.write( "\n" ); document.write( " - Introduction to Permutations\r \n" ); document.write( "\n" ); document.write( " - PROOF of the formula on the number of Permutations\r \n" ); document.write( "\n" ); document.write( " - Problems on Permutations\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " - OVERVIEW of lessons on Permutations and Combinations\r \n" ); document.write( "\n" ); document.write( "in this site.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-II in this site\r \n" ); document.write( "\n" ); document.write( " - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Combinatorics: Combinations and permutations\". \r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II \n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |