document.write( "Question 360325: In a random arrangement of letters of word VIOLENT how many ways are there that the vowels occupy odd positions only \n" ); document.write( "
Algebra.Com's Answer #257193 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "The other tutor made it unnecessarily complicated.\r\n" );
document.write( "\r\n" );
document.write( "There are 3 vowels: I, O, E \r\n" );
document.write( "\r\n" );
document.write( "and \r\n" );
document.write( "\r\n" );
document.write( "there are 4 consonants V, L, N, T\r\n" );
document.write( "\r\n" );
document.write( "and\r\n" );
document.write( "\r\n" );
document.write( "there are 4 odd positions: 1st letter, 3rd letter, 5th letter, 7th letter.\r\n" );
document.write( "\r\n" );
document.write( "So we choose 3 of the 4 odd positions for the vowels in 4C3 or 4 ways.\r\n" );
document.write( "Having chosen which of the 3 odd positions the 3 vowels are to go in, \r\n" );
document.write( "we can then arrange the three vowels in those odd positions in 3P3 \r\n" );
document.write( "or 3! ways.  \r\n" );
document.write( "Having placed the vowels, the other 4 positions are filled with the \r\n" );
document.write( "4 consonants in 4P4 or 4! ways.\r\n" );
document.write( "\r\n" );
document.write( "That's 4*3!*4! = 576\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );