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?

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