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

A. 30

B. 48

C. 144

D. 576

E. None of these

**Answer: Option D **

__Solution(By Examveda Team)__

The given word contains 7 different letters.Keeping the vowels (AUIO) together, we take them as 1 letter.

Then, we have to arrange the letters CTN (AUIO).

Now, 4 letters can be arranged in 4! = 24 ways.

The vowels (AUIO) can be arranged among themselves in 4! = 24 ways.

∴ Required number of ways = (24 × 24) = 576

Related Questions on Permutation and Combination

A. 3! 4! 8! 4!

B. 3! 8!

C. 4! 4!

D. 8! 4! 4!

A. 7560,60,1680

B. 7890,120,650

C. 7650,200,4444

D. None of these

A. 8 × 9!

B. 8 × 8!

C. 7 × 9!

D. 9 × 8!

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