document.write( "Question 857822: how many different arrangement of the letters in the word \"ellipses\" can be formed if the consonants must be together? \n" ); document.write( "

Algebra.Com's Answer #517031 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "\"ellipses\" has consonants l,l,p,s,s and vowels e,i,e\r\n" );
document.write( "\r\n" );
document.write( "First we find the number of ways positions can be chosen\r\n" );
document.write( "to make sure the 5 consonants are together:\r\n" );
document.write( "\r\n" );
document.write( "There are the following 4 ways of choosing positions 1 through 8\r\n" );
document.write( "to be held by consonants and vowels.  There are these four with \r\n" );
document.write( "the 5 consonants together:\r\n" );
document.write( " \r\n" );
document.write( "CCCCCVVV, VCCCCCVV, VVCCCCCV, and VVVCCCCC\r\n" );
document.write( "\r\n" );
document.write( "For each of those 4 choices of positions to be held by \r\n" );
document.write( "consonants and vowels,\r\n" );
document.write( "\r\n" );
document.write( "there are  = 30  ways to arrange the consonants since the\r\n" );
document.write( "2 l's are indistinguishable and the two s's are indistinguishable,\r\n" );
document.write( "\r\n" );
document.write( "and there are  = 3 ways to arrange the vowels since the 2 e's\r\n" );
document.write( "are indistinguishable.\r\n" );
document.write( "\r\n" );
document.write( "Answer 4×30×3 = 360 \r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( " \n" ); document.write( "

\n" );