First slide

Permutations

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

Moderate

A

3600
B

4200
C

3680
D

None of these

Solution

There are eleven letters in the word ‘Pataliputra’ and there are two p’s, two r’s, three a’s and four other different letters.
Number of consonants = 6, number of vowels = 5.
Since relative order of the vowels and consonants remains 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 vowels can be arranged among themselves in $\frac{5!}{3!}$ ways, since a occurs thrice.
$∴ Required number = \frac{6!}{2! 2!} \cdot \frac{5!}{3!} = 3600$ .

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