Question

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

• A. $720$
• B. $1800$
• C. $3600$
• D. $4320$

Answer 1

The correct option is C $3600$

Note that the word $PATALIPUTRA$ has the vowels at 2nd, 4th, 6th, 8th and 11th position. In the new arrangement of the letters, the vowels will be at the same positions.
Hence the 5 vowels can be arrange among themselves in $\frac{5!}{3!}$ as the letter A is repeated thrice.
The remaining 6 consonants can be permute among themselves in $\frac{6!}{2!2!}$ as the two letters, P and T are repeated twice.
Hence the total number of permutations are$\frac{6!}{2!2!}\times \frac{5!}{3!}=3600$