How many new words can be formed using all the letters of the word 'MEDITERRANEAN', if vowels and consonants occupy the same relative positions ?

Answer

`(7!)/(2!2!)xx(6!)/(3!2!)`

Explanation

Consonants M, D, T, R, R, N, N can be arranged in positions 1, 3,5,7,8,10, 13 in `(7!)/(2!2!)` ways.
Vowels E,I,E,A,E,A can be arranged in positions 2,4,6,9,11,12 in `(6!)/(3!2!)` ways.
So, total number of ways`=(7!)/(2!2!)xx(6!)/(3!2!)`.