SOLUTION: How many possible arrangements of the 6 letters in the word BEAUTY if the 3 vowels are together?

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Question 1191840: How many possible arrangements of the 6 letters in the word BEAUTY if the 3 vowels are together?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Choose an arrangement of the three vowels {E,A,U} in 3! ways. 

Let X represent the arrangement of {E,A,U} that you chose.

For each of those possible 3! choices of vowel arrangement, 
we can choose an arrangement of {B,X,T,Y} any of 4! ways.

Answer: (3!)(4!)

Edwin