Question

The number of words that can be formed, with the letters of the work $PATALIPUTRA$ without changing the relative order of the vowels and consonants is

• A. $3600$
• B. $4200$
• C. $3680$
• D. None of these

Answer 1

Answer: (A)

$3600$

There are $11$ letters in the given word $2P,2T,3A$ and $4$ other different letters.

Number of Vowels $=5$, consonants $=6$

Since the relative order of the vowels and consonants remain unchanged, thus vowels will occupy only vowel's place and consonants will occupy only consonant's place. So $6$ consonants can be arranged among themselves in $\frac{6!}{2!2!}$ ways (as there are $2P$ and $2T$)

and $5$ vowels can be arranged among themselves in $\frac{5!}{3!}$ ways as a occurs thrice.

So required numbers $\frac{5!}{3!}\times \frac{6!}{2!2!}=3600$