Relative Positon

There are eleven letters in the word $PATLIPUTRA$ and there are two $P$ 's, two $T$ 's and three $A$ 's and four other different letters.

Number of consonants $=6$ , number of vowels $=5$ Since the relative order of vowels and consonants remain unchanged, therefore, vowels will occupy only vowel's place and consonants will occupy only consonant's place.

Now 6 consonants can be arranged among themselves in $\frac { 6! }{ 2!2! }$ ways (since there are two $P$ 's and two $T$ 's )

and five vowles can be arranged among themselves in

$\frac {5!}{3!}$ ways since $A$ occurs thrice

$\therefore$ Required number $=\frac { 6! }{ 2!2! }\times \frac {5!}{3!}=3600$