document.write( "Question 891927: A boat is to b manned by 8 men,of whom,one cannot row on the bow side and two cannot row on the stroke side. In how many ways can the crew be arranged? \n" ); document.write( "
Algebra.Com's Answer #540162 by Edwin McCravy(20055)![]() ![]() You can put this solution on YOUR website! \r\n" ); document.write( "We will label the 1 man who cannot row on the bow side S, \r\n" ); document.write( "since he must row on the stroke side.\r\n" ); document.write( "\r\n" ); document.write( "We will label the 2 men who cannot row on the stroke side B, \r\n" ); document.write( "since they must row on the bow side.\r\n" ); document.write( "\r\n" ); document.write( "We will label the other 5 men BS, since they can row on\r\n" ); document.write( "either side.\r\n" ); document.write( "\r\n" ); document.write( "So the men are labeled:\r\n" ); document.write( "\r\n" ); document.write( "S,B,B,BS,BS,BS,BS,BS\r\n" ); document.write( "\r\n" ); document.write( "So the boat is manned this way:\r\n" ); document.write( "\r\n" ); document.write( "Bow side: B,B,BS,BS\r\n" ); document.write( "Stroke side: S,BS,BS,BS\r\n" ); document.write( "\r\n" ); document.write( "We choose 2 BS's for the bow side in C(5,2) = 10 ways,\r\n" ); document.write( "and the other three will be on the stroke side.\r\n" ); document.write( "\r\n" ); document.write( "For each of those choices there are 4! or 24 ways to rearrange\r\n" ); document.write( "the men on the bow side, and 4! or 24 ways to rearrange the men\r\n" ); document.write( "on the stroke side. \r\n" ); document.write( "\r\n" ); document.write( "Answer: C(5,2)*4!*4! = 10*24*24 = 5760 ways.\r\n" ); document.write( "\r\n" ); document.write( "Edwin\n" ); document.write( " |