document.write( "Question 891977: consider strings of length 10 which contain only letters from the set{A,E,I,O,U} and digits from {1,3,5,7,9}suppose repetition of letters is not allowed.
\n" ); document.write( "a) how many different strings are there?
\n" ); document.write( "b) How many different strings are there if the letters,i.e A,E,I,O,U and the digits,i.e 1,3,5,7,9 must alternate?
\n" ); document.write( "c) How many different strings are there if all five letters must be adjacent in each string? \n" ); document.write( "

Algebra.Com's Answer #540186 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!
consider strings of length 10 which contain only letters from the set{A,E,I,O,U} and digits from {1,3,5,7,9}suppose repetition of letters is not allowed.
\n" ); document.write( "a) how many different strings are there?
\n" ); document.write( "

\r\n" );
document.write( "P(10,10) = 10! = 3628800\r\n" );
document.write( "

\n" ); document.write( "b) How many different strings are there if the letters,i.e A,E,I,O,U and the digits,i.e 1,3,5,7,9 must alternate?
\n" ); document.write( "

\r\n" );
document.write( "They can go either\r\n" );
document.write( "\r\n" );
document.write( "LDLDLDLDLD or DLDLDLDLDL, where D stands for a digit and L for a letter.\r\n" );
document.write( "\r\n" );
document.write( "There are P(5,5) = 5! = 120 ways the letters can be arranged times\r\n" );
document.write( "P(5,5) = 5! = 120 ways the digits can be arranged.  Then we multiply by\r\n" );
document.write( "2 because we can either start with a letter or a digit.\r\n" );
document.write( "\r\n" );
document.write( "Answer:  5!*5!*2 = 120*120*2 = 28800.\r\n" );
document.write( "

\n" ); document.write( "c) How many different strings are there if all five letters must be adjacent in each string?
\n" ); document.write( "

\r\n" );
document.write( "Think of (AEIOU) as a single thing.  Then there are these 6 things\r\n" );
document.write( "to rearrange:\r\n" );
document.write( "\r\n" );
document.write( "1,3,5,7,9,(AEIOU)\r\n" );
document.write( "\r\n" );
document.write( "which is P(6,6) = 6! = 720.  But we must multiply this by P(5,5) = 5! since the\r\n" );
document.write( "letters (AEIOU) can be rearranged in 5! ways.\r\n" );
document.write( "\r\n" );
document.write( "Answer 6!*5! = 720*120 = 86400 \r\n" );
document.write( "\r\n" );
document.write( "Edwin

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

\n" );