Question

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. 6
• B. 13
• C. 12
• D. 14
• E. 15

Answer 1

The correct option is C

12

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

The vowels occupy 3^rd, 5^th, 7^thand 8^thposition 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 aforementioned 4 places and the consonants can occupy 1^st, 2^nd, 4^th, 6^thand 9^thpositions.

The 4 vowels can be arranged in the 3^rd, 5^th, 7^thand 8^thposition in 4! ways.
Similarly, the 5 consonants can be arranged in 1^st, 2^nd, 4^th, 6^thand 9^thposition in 5! ways.

Hence, the total number of ways = 4! $\times$ 5!