document.write( "Question 872190: How many different arrangements of four books on a shelf could you make from eight books? \n" ); document.write( "
Algebra.Com's Answer #525974 by Edwin McCravy(20055)![]() ![]() You can put this solution on YOUR website! \r\n" ); document.write( "You can choose the first book any of 8 ways,\r\n" ); document.write( "\r\n" ); document.write( "For each of those 8 ways to choose the first book,\r\n" ); document.write( "you can then choose the second book any of the 7 remaining ways.\r\n" ); document.write( "That's 8×7 or 56 ways to choose the first two books.\r\n" ); document.write( "\r\n" ); document.write( "For each of those 8×7 or 56 ways to choose the first two books,\r\n" ); document.write( "you can then choose the third book any of the 6 remaining ways.\r\n" ); document.write( "That's 8×7×6 or 336 ways to choose the first three books.\r\n" ); document.write( "\r\n" ); document.write( "For each of those 8×7×6 or 336 ways to choose the first three books,\r\n" ); document.write( "you can then choose the fourth book any of the 5 remaining ways.\r\n" ); document.write( "That's 8×7×6×5 or 1680 ways to choose the four books.\r\n" ); document.write( "\r\n" ); document.write( "Answer: 1680\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "This is a permutation problem since order of the books matters\r\n" ); document.write( "\r\n" ); document.write( "That's the permutations of 8 things taken 4 at a time\r\n" ); document.write( "\r\n" ); document.write( "On the TI-83 and 84 calculators, that's 8 nPr 4.\r\n" ); document.write( "\r\n" ); document.write( "Here's how:\r\n" ); document.write( "\r\n" ); document.write( "Press ON\r\n" ); document.write( "Press CLEAR\r\n" ); document.write( "Press 8\r\n" ); document.write( "Press MATH\r\n" ); document.write( "Press the left arrow key\r\n" ); document.write( "Press 2\r\n" ); document.write( "press 4\r\n" ); document.write( "Press ENTER\r\n" ); document.write( "\r\n" ); document.write( "You will see\r\n" ); document.write( "\r\n" ); document.write( "8 nPr 4 \r\n" ); document.write( " 1680\r\n" ); document.write( "\r\n" ); document.write( "Edwin\n" ); document.write( " |