document.write( "Question 658958: If the letter 'Daughter' are to be arranged so that vowels occupy odd places, then number of different word are \n" ); document.write( "
Algebra.Com's Answer #410613 by Edwin Parker(36)![]() ![]() ![]() You can put this solution on YOUR website! \r\n" ); document.write( "\r\n" ); document.write( "[There are only 3 vowels, a,u, and e, and there are 4 odd places. So\r\n" ); document.write( "one of the odd spaces must contain a consonant.]\r\n" ); document.write( "\r\n" ); document.write( "we can choose 3 of the 4 odd places to put the vowels in C(4,3) or 4 ways.\r\n" ); document.write( "\r\n" ); document.write( "For each of those we can rearrange the vowels in P(3,3) or 3! or 6 ways.\r\n" ); document.write( "\r\n" ); document.write( "And we can rearrange the 5 consonants in P(5,5) or 5! or 120 ways.\r\n" ); document.write( "\r\n" ); document.write( "C(4,3)稰(3,3)稰(5,5) = 420 = 2880 ways.\r\n" ); document.write( "\r\n" ); document.write( "Edwin\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \r \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |