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In how many ways can the letters of the word PATLIPUTRA be arranged, so that the relative order of vowels and consonants do not alter?

In how many ways can the letters of the word PATLIPUTRA be arranged, so that the relative order of vowels and consonants do not alter?

Grade:12th pass

1 Answers

Arun
25750 Points
6 years ago
The word PATALIPUTRA has total 11 characters. Out of them, 
5 are Vowels (A A I U A) occupying positions 2,4,6,8,11
6 are consonants (P T L P T R) occupying positions 1,3,4,5,8,9
 
Relative order of vowels and consonants cannot be changed.
 i.e., position of vowels and consonants cannot be changed

5 vowels can be arranged in 5! / 3! ways  (we divide by 3! as there are 3 'A')

6 consonants can be arranged in 6! / 2!×2! ways (we divide by (2! × 2!) as there are 2 'P' and 2 'T')

Total number of ways = (5!/ 3!)×(6!/2!×2!)=20×180=3600

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