SOLUTION: In how many different ways can the letters of the word KNOWLEDGE be arranged in such a way that the vowels always come together?

Question 1164692: In how many different ways can the letters of the word KNOWLEDGE be arranged
in such a way that the vowels always come together?
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!
In how many different ways can the letters of the word KNOWLEDGE be arranged
in such a way that the vowels always come together?

We can choose the 3 vowels to be together (call it a "vowel trio") any of
these 3 ways: EEO, EOE, OEE.

For each of those 3 choices, there are 7 things (six single letters and one
vowel-trio).  The 7 things are

K, N, W, L, D, G, (the vowel trio)

There are 7! ways to arrange those seven things:

Answer: 3∙7! = 3∙5040 = 15120 ways.

Edwin

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