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09 Feb 2021, 05:45
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
53% (02:08) correct
48%
(02:24)
wrong
based on 120
sessions
History
Date
Time
Result
Not Attempted Yet
How many words can be formed with the letters of the word PATALIPUTRA without changing the relative order of the vowels and consonants?
A. 900
B. 1800
C. 3600
D. 7200
E. 10800
A. 900
B. 1800
C. 3600
D. 7200
E. 10800
13 Feb 2021, 23:48
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Not changing the relative order means keeping the vowels and consonants in the same place as the original word.
In P A T A L I P U T R A, the consonants an vowels are C V C V C V C V C C V
We have 6 consonants of which P comes twice and T comes twice.
The number of arrangements for the consonants = 6! / 2!2! = 180
We have 5 vowels of which A is repeated thrice
The number of arrangements for the vowels = 5! / 3! = 20
Total number of words = 180 * 20 = 3600
Option C
Arun Kumar
In P A T A L I P U T R A, the consonants an vowels are C V C V C V C V C C V
We have 6 consonants of which P comes twice and T comes twice.
The number of arrangements for the consonants = 6! / 2!2! = 180
We have 5 vowels of which A is repeated thrice
The number of arrangements for the vowels = 5! / 3! = 20
Total number of words = 180 * 20 = 3600
Option C
Arun Kumar
18 Feb 2021, 11:24
Kudos
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Bunuel
Solution:
We see that the relative order of the vowels and consonants of the word PATALIPUTRA is CVCVCVCVCCV where a consonant is denoted by C and a vowel by V. Therefore, the six consonants can be arranged in 6!/(2! x 2!) = 720/4 = 180 ways (notice that we divide by 2! x 2! because there are 2 P’s and 2 T’s). Likewise, the 5 vowels can be arranged in 5!/3! = 120/6 = 20 ways (notice that we divide by 3! because there are 3 A’s). Therefore, there are 180 x 20 = 3600 ways to arrange the letters of the word PATALIPUTRA without changing the relative order of the vowels and consonants.
Answer: C
