Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 202523 JanuaryMorning Shift
Exam
JEE Main
Year
2025
Date
23 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Permutation and Combination

JEE Main 2025 · 23 January · Morning Shift · Mathematics · Permutation and Combination

The number of words, which can be formed using all the letters of...

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

Options

  1. A3600036000
  2. B3700037000
  3. C3400034000
  4. D3500035000

Correct answer

A. 3600036000

Step-by-step solution

DAUGHTER Total words =8=8 ! Total words in which vowels are together =6!×3!=6!\times 3! words in which all vowels are not together =8!−6!×3!=6![56−6]=720×50=36000\begin{aligned} & =8!-6!\times 3! \\ & =6![56-6] \\ & =720 \times 50 \\ & =36000 \end{aligned} Ans.(3)
Practice Permutation and Combination on Quantrex Academy →

More from Permutation and Combination

All Permutation and Combination questions Full Permutation and Combination list Permutation and Combination JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs