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In how many ways the letters of the word triangle be arranged in such a way that vowels do not comes together?
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In how many ways the letters of the word triangle be arranged in such ...
Arrangement of Letters in the Word 'Triangle' without Vowels Together
- Total number of ways to arrange the letters in the word 'triangle'
The word 'triangle' has 8 letters in total. Therefore, the total number of ways to arrange these letters is 8!.
- Number of ways to arrange the vowels (i, a, e) together
Since the vowels (i, a, e) have to be together, we can consider them as one entity. This entity has 3! ways of arrangement among themselves.
- Number of ways to arrange the consonants (t, r, n, g, l) and the entity of vowels
Now, we have 5 entities to arrange - t, r, n, g, l, and the entity of vowels (i, a, e). This gives us a total of 6 entities. Therefore, the number of ways to arrange them is 6!.
- Final calculation
To find the total number of ways where the vowels do not come together, we subtract the number of ways where the vowels come together from the total number of ways:
Total ways = 8!
Ways with vowels together = 3! * 6!
Required ways = 8! - (3! * 6!)
- Calculation
8! - (3! * 6!) = 40,320 - (6 * 720) = 40,320 - 4,320 = 36,000
Therefore, there are 36,000 ways to arrange the letters of the word 'triangle' such that the vowels do not come together.
- Total number of ways to arrange the letters in the word 'triangle'
The word 'triangle' has 8 letters in total. Therefore, the total number of ways to arrange these letters is 8!.
- Number of ways to arrange the vowels (i, a, e) together
Since the vowels (i, a, e) have to be together, we can consider them as one entity. This entity has 3! ways of arrangement among themselves.
- Number of ways to arrange the consonants (t, r, n, g, l) and the entity of vowels
Now, we have 5 entities to arrange - t, r, n, g, l, and the entity of vowels (i, a, e). This gives us a total of 6 entities. Therefore, the number of ways to arrange them is 6!.
- Final calculation
To find the total number of ways where the vowels do not come together, we subtract the number of ways where the vowels come together from the total number of ways:
Total ways = 8!
Ways with vowels together = 3! * 6!
Required ways = 8! - (3! * 6!)
- Calculation
8! - (3! * 6!) = 40,320 - (6 * 720) = 40,320 - 4,320 = 36,000
Therefore, there are 36,000 ways to arrange the letters of the word 'triangle' such that the vowels do not come together.
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In how many ways the letters of the word triangle be arranged in such a way that vowels do not comes together?
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In how many ways the letters of the word triangle be arranged in such a way that vowels do not comes together? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In how many ways the letters of the word triangle be arranged in such a way that vowels do not comes together? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In how many ways the letters of the word triangle be arranged in such a way that vowels do not comes together?.
In how many ways the letters of the word triangle be arranged in such a way that vowels do not comes together? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In how many ways the letters of the word triangle be arranged in such a way that vowels do not comes together? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In how many ways the letters of the word triangle be arranged in such a way that vowels do not comes together?.
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