Q. 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
Explanation
[Solution by Dr. Abubacker] Total arrangements $=8!=40320$. With the 3 vowels (A, U, E) together: $6!\times3!=4320$. Required $=40320-4320=36000$. Answer (1).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.