JEE Mains · Maths · STD 11 - 6. permutation and combination
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
- A \(36000\)
- B \(37000\)
- C \(34000\)
- D \(35000\)
Answer & Solution
Correct Answer
(A) \(36000\)
Step-by-step Solution
Detailed explanation
DAUGHTER Total words \(=8\) ! Total words in which vowels are together \(=6!\times 3!\) words in which all vowels are not together \(\begin{aligned} & =8!-6!\times 3! \\ & =6![56-6] \\ & =720 \times 50 \\ & =36000 \end{aligned}\) Ans.(3)
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