Question

N how many different ways can the letters of the word geometry be arranged so that the vowels always come together?

Answer 1

Hi there!
Here's the answer :

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Given
Word = GEOMETRY


Vowels in the given word are : EOE

All the vowels in the given word are treated as a single letter (EOE)

Remaining are the consonants: G M T R Y

Now there are 6 letters :
5 consonants + 1 vowel unit

¶ G M T R Y (EOE)

• No. of ways of arranging these letters = 6! = 720

- Now, EOE has 3 letter out of which E occurs 2 times and the other letter is a different one that is O

• No. of ways of arranging these letters = 3!/2! = 3

•°• Required No. of words = (720 × 3) = 2160



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