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How many total words can be formed from the letters of the word INSURANCE in which vowels are always together?

  • a)
    9680

  • b)
    17280

  • c)
    12780

  • d)
    8640

Correct answer is option 'D'. Can you explain this answer?
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How many total words can be formed from the letters of the word INSURA...
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How many total words can be formed from the letters of the word INSURA...
Approach:
To find the total number of words that can be formed from the letters of the word 'INSURANCE' such that vowels are always together, we can consider the vowels (I, U, A, E) as a single entity. Therefore, the total number of letters to be arranged becomes 5 (NSRNC) + 1 (Vowels) = 6.

Calculation:
- Total number of ways to arrange 6 letters (6!) = 720
- The vowels can be arranged among themselves in 4! ways = 24
- Therefore, the total number of ways to arrange the word 'INSURANCE' with vowels together = 720 * 24 = 17280

Final Answer:
Therefore, the total number of words that can be formed from the letters of the word 'INSURANCE' with vowels always together is 17280. Hence, the correct answer is option 'D'.
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How many total words can be formed from the letters of the word INSURANCE in which vowels are always together?a)9680b)17280c)12780d)8640Correct answer is option 'D'. Can you explain this answer?
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