# In how many ways can the letters of the word **EDUCATION** be rearranged so that the relative position of the vowels and consonants remain the same as in the word **EDUCATION**?

A. 9! × 4

B. 9! × 4! × 5!

C. 4! × 5!

D. None of these

**Answer: Option C **

__Solution(By Examveda Team)__

The word **EDUCATION**is a 9 letter word, with none of the letters repeating.

The vowels occupy 3

^{rd}, 5

^{th}, 7

^{th}and 8

^{th}position in the word and the remaining 5 positions are occupied by consonants.

As the relative position of the vowels and consonants in any arrangement should remain the same as in the word EDUCATION, the vowels can occupy only the before mentioned 4 places and the consonants can occupy 1

^{st}, 2

^{nd}, 4

^{th}, 6

^{th}and 9

^{th}positions.

The 4 vowels can be arranged in the 3

^{rd}, 5

^{th}, 7

^{th}and 8

^{th}position in 4! Ways.

Similarly, the 5 consonants can be arranged in 1

^{st}, 2

^{nd}, 4

^{th}, 6

^{th}and 9

^{th}

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## Comments ( 2 )

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!

Ans 78796857

It's contain 4 consonants and 5 vowels not 5 consonants and 4 vowels