Question 885951
<pre>
The three-letter words are of these types VVV, VCV, CVV

Case 1:  VVV
Choose the first vowel any of 5 ways
Choose the second vowel any of 5 ways
Choose the third vowel any of 5 ways.

That's 5*5*5 = 125 ways.

Case 2:  VCV
Choose the first vowel any of 5 ways
Choose the consonant any of 7 ways
Choose the remaining vowel any of 5 ways.

That's 5*7*5 = 175 ways.

Case 3:  CVV
Choose the consonant any of 7 ways
Choose the first vowel any of 5 ways
Choose the remaining vowel any of 5 ways.

That's 5*5*7 = 175 ways.

Total = 125 + 175 + 175 = 475 ways.

Edwin</pre>