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 :
JEE · Math · previous-year question
- A.34000
- B.37000
- C.35000
- D.36000correct
Answer
D. 36000
Explanation
DAUGHTER Total words $=8$ ! Total words in which vowels are together $=6!\times 3!$ words in which all vowels are not together $$\begin{aligned} & =8!-6!\times 3! \\ & =6![56-6] \\ & =720 \times 50 \\ & =36000 \end{aligned}$$
Practice more JEE questions
Answer thousands more real JEE previous-year questions free, get graded instantly, and climb the global ranked leaderboard.
Practice JEE free →More JEE Math questions
- What is the total number of distinct x \in \mathbb{R} for which \left|\begin{array}{ccc}x …
- Let m be the smallest positive integer such that the coefficient of x^{2} in the expansion…
- What is the total number of distinct x \in[0,1] for which \int_{0}^{x} \frac{t^{2}}{1+t^{4…
- Let \alpha, \beta \in \mathbb{R} be such that \lim _{x \rightarrow 0} \frac{x^{2} \sin (\b…
- Let z=\frac{-1+\sqrt{3} i}{2}, where i=\sqrt{-1}, and r, s \in\{1,2,3\}. Let P=\left[\begi…
- For how many values of p, the circle x^{2}+y^{2}+2 x+4 y-p=0 and the coordinate axes have …
- Let f: \mathbb{R} \rightarrow \mathbb{R} be a differentiable function such that f(0)=0, f\…
- For a real number \alpha, if the system \[ \left[\begin{array}{ccc} 1 & \alpha & \alpha^{2…