How many words can be formed with the letters of thw word 'PATALIPUTRA' without changing the relative positions of vowels and consonants?

Explanation

The word 'PATALIPUTRA' has eleven letters, in which 2P's, 3A's, 2T's, 1L, 1U, 1R and 1I. Vowels are AAIUA
These vowels can be arranged themselves in `(5!)/(3!)=`20 ways
the consonants are PTLPTR these consonants can be
arranged themselves in `(6!)/(2!2!)=180` ways.
`therefore`Required number of words
`=20xx180=3600` ways.