document.write( "Question 1173525: How many ways are there for 5 men and seven women to stand in a line so that three women
\n" );
document.write( "stand next to each other \n" );
document.write( "
Algebra.Com's Answer #798738 by ikleyn(52781)![]() ![]() You can put this solution on YOUR website! . \n" ); document.write( "How many ways are there for 5 men and seven women to stand in a line so that three \n" ); document.write( "stand next to each other \n" ); document.write( "~~~~~~~~~~~~~\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \r\n" ); document.write( "From the remote point of view, you consider these 3 women as one clued object.\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "So the total number of object to permute, from this point of view is 5 + 7 - 2 = 10.\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "For 10 objects, you have 10! = 10*9*8*7*6*5*4*3*2*1 = 3628800 permutations.\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "Now, from the close point of view, there are 3! = 3*2*1 = 6 possible permutations inside this group of the 3 women.\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "It gives the total 6*3628800 = 10886400 possible permutationns. ANSWER\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( " \n" ); document.write( " |