SOLUTION: The Hawaiian alphabet consists of 7 consonants and 5 vowels. How many three letter words are possible if there are never two consonants together and if a word must always end in a

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Question 885951: The Hawaiian alphabet consists of 7 consonants and 5 vowels. How many three letter words are possible if there are never two consonants together and if a word must always end in a vowel ?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
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