Book Online Demo
Check Your IQ
Try Test

Courses

Dropper NEET CourseDropper JEE CourseClass - 12 NEET CourseClass - 12 JEE CourseClass - 11 NEET CourseClass - 11 JEE CourseClass - 10 Foundation NEET CourseClass - 10 Foundation JEE CourseClass - 10 CBSE CourseClass - 9 Foundation NEET CourseClass - 9 Foundation JEE CourseClass -9 CBSE CourseClass - 8 CBSE CourseClass - 7 CBSE CourseClass - 6 CBSE Course

Q.

Find the number of different 8− letter arrangements that can be made from the letters of the word “DAUGHTER” such that all vowels do not occur together.


see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!
An Intiative by Sri Chaitanya

a

36000

b

4320

c

10080

d

40230 

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Total number of letters in DAUGHTER = 8
Total number of permutations of 8 letters = 8P8 = 40320
And vowels in DAUGHTER=A, V and E.
Since all vowels occur together, assume AUE as a single object and left letters are DGHTR
Arrange 3 vowels = 3P3 = 720
Arrange 6 letters = 6P6 = 4320
All vowels do not occur together =total number of permutations – number of permutations of all vowels occurring together =40320 – 4320 = 36000
Hence, Option (1) is the correct answer.
  
Watch 3-min video & get full concept clarity

tricks from toppers of Infinity Learn

Related Blogs
Get ₹ 1 crore* worth scholarship for JEE / NEET / Foundation
Result Producing online coaching for JEE/NEET of south India
Largest All India Test Series for JEE/NEET
Best Books for IIT JEE
Best Books for NEET
score_test_img

Get Expert Academic Guidance – Connect with a Counselor Today!

Related Blogs
Get ₹ 1 crore* worth scholarship for JEE / NEET / Foundation
Result Producing online coaching for JEE/NEET of south India
Largest All India Test Series for JEE/NEET
Best Books for IIT JEE
Best Books for NEET
whats app icon
Find the number of different 8− letter arrangements that can be made from the letters of the word “DAUGHTER” such that all vowels do not occur together.