document.write( "Question 837915: Find the total number of 4 letter words which have a
\n" ); document.write( "vowel only as the first and the last letter.
\n" ); document.write( "

Algebra.Com's Answer #505369 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "There are four cases.\r\n" );
document.write( "\r\n" );
document.write( "1.  Like EJXA.  The 2 vowels distinguishable and the 2 consonants distinguishable.\r\n" );
document.write( "\r\n" );
document.write( "Choose the beginning vowel letter 5 ways, the last vowel 4 ways, the first\r\n" );
document.write( "consonant 21 ways and the other consonant 20 ways.\r\n" );
document.write( "\r\n" );
document.write( "That's 5×4×21×20 = 8400 \r\n" );
document.write( "\r\n" );
document.write( "2.  Like UZPU.  The 2 vowels indistinguishable and the 2 consonants distinguishable.\r\n" );
document.write( "\r\n" );
document.write( "Choose the same vowel for the first and last letter 5 ways. Choose the first\r\n" );
document.write( "consonant 21 ways and the other consonant 20 ways.\r\n" );
document.write( "\r\n" );
document.write( "That's 5×21×20 = 2100 \r\n" );
document.write( "\r\n" );
document.write( "3. Like IKKO.  The 2 vowels distinguishable and the 2 consonants indistinguishable.\r\n" );
document.write( "\r\n" );
document.write( "Choose the beginning vowel letter 5 ways, the last vowel 4 ways. Choose the\r\n" );
document.write( "same consonant for the middle letters 21 ways.\r\n" );
document.write( "\r\n" );
document.write( "That's 5×4×21 = 420 \r\n" );
document.write( "\r\n" );
document.write( "4.  Like ARRA.  The 2 vowels indistinguishable and the 2 consonants\r\n" );
document.write( "indistinguishable.\r\n" );
document.write( "\r\n" );
document.write( "Choose the same vowel for the first and last letter 5 ways. Choose the same\r\n" );
document.write( "consonant for the middle letters 21 ways.\r\n" );
document.write( "\r\n" );
document.write( "That's 5×21 = 105\r\n" );
document.write( "\r\n" );
document.write( "Total = 8400+2100+420+105 = 11025.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );