SOLUTION: Find the total number of 4 letter words which have a vowel only as the first and the last letter.

There are four cases.

1.  Like EJXA.  The 2 vowels distinguishable and the 2 consonants distinguishable.

Choose the beginning vowel letter 5 ways, the last vowel 4 ways, the first
consonant 21 ways and the other consonant 20 ways.

That's 5×4×21×20 = 8400 

2.  Like UZPU.  The 2 vowels indistinguishable and the 2 consonants distinguishable.

Choose the same vowel for the first and last letter 5 ways. Choose the first
consonant 21 ways and the other consonant 20 ways.

That's 5×21×20 = 2100 

3. Like IKKO.  The 2 vowels distinguishable and the 2 consonants indistinguishable.

Choose the beginning vowel letter 5 ways, the last vowel 4 ways. Choose the
same consonant for the middle letters 21 ways.

That's 5×4×21 = 420 

4.  Like ARRA.  The 2 vowels indistinguishable and the 2 consonants
indistinguishable.

Choose the same vowel for the first and last letter 5 ways. Choose the same
consonant for the middle letters 21 ways.

That's 5×21 = 105

Total = 8400+2100+420+105 = 11025.

Edwin