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Examveda

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 3rd, 5th, 7th and 8th 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 1st, 2nd, 4th, 6th and 9th positions.

The 4 vowels can be arranged in the 3rd, 5th, 7th and 8th position in 4! Ways.

Similarly, the 5 consonants can be arranged in 1st, 2nd, 4th, 6th and 9th

This Question Belongs to Arithmetic Ability >> Permutation And Combination

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Comments ( 2 )

  1. Sounok Pal
    Sounok Pal :
    10 months ago

    Ans 78796857

  2. Akash Kumar
    Akash Kumar :
    3 years ago

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

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