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The number of words, which can be formed using all the letters of the word “DAUGHTER”, so that all the vowels never come together, is

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37000

36000

34000

35000

answer is C.

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Detailed Solution

Total number of words that can be made using the word DAUGHTER IS $8!$

Total number of words in which vowels are together = $6! \times 3!$

Number of words in which vowels are not together= $8! - 6! 3! = 6! (56 - 6) = 720 \times 50 = 36000$

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