CBSE Class 11-science Answered
Find the number of different 8-letter arrangements that can be made from the letters of the word DAUGHTER so that:
a.all vowels occur together.
b.all vowels do not occur together.
Asked by pragati nargotra | 07 Mar, 2014, 08:40: PM
Expert Answer
The vowels are A, U and E.
a.
Considering three vowels as one letter, we have 6 letters, D, AUE, G, H, T, R
These six letters can be arranged in 
ways.
ways.But the vowels can be put together in 3! ways.
Thus, the total number of arrangements 
b.
There are 8 letters in the word "DAUGHTER"
Thus, the total number of words formed by using all eight letters is 
Therefore, the total number of ways in which all vowels do not occur together
= Total number of words - Number of arrangements in which all vowels are together
=40320 - 4320 = 36000
Answered by | 08 Mar, 2014, 09:00: AM
Concept Videos
-
Fundamental Principle of Counting
This video explains the fundamental principles of counting, Multiplicati...
-
Combinations
This video explains the derivation of the formula of combination, different... -
Permutations: Distinct Objects
This video explains the permutation of n objects taken r at a time, factori... -
Application on arrangements of objects using n!/(P1!P2! ...
Formulate the theorem of permutation on n objects when all objects are not ... -
Revising concepts and theorems of permutation and combi ...
Review the concepts and theorems of permutation and combinations. Solve pro...
CBSE 11-science - Maths
Asked by kanhaparashar17 | 04 Apr, 2024, 12:55: PM
ANSWERED BY EXPERTCBSE 11-science - Maths
Asked by tharshini8456157 | 27 Nov, 2023, 10:32: PM
ANSWERED BY EXPERTCBSE 11-science - Maths
Asked by lavanya.toshit | 21 Feb, 2023, 09:16: PM
ANSWERED BY EXPERTCBSE 11-science - Maths
Asked by pranshusingh9himalya | 15 Nov, 2022, 01:43: AM
ANSWERED BY EXPERTCBSE 11-science - Maths
Asked by ismayilpmamu | 09 Apr, 2020, 10:10: PM
ANSWERED BY EXPERTCBSE 11-science - Maths
Asked by kandappan | 10 Feb, 2020, 05:34: PM
ANSWERED BY EXPERTCBSE 11-science - Maths
Asked by Kchawla94 | 28 Feb, 2019, 08:07: PM
ANSWERED BY EXPERTCBSE 11-science - Maths
Asked by Kashifimam866 | 20 Feb, 2019, 05:58: AM
ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by lovemaan5500 | 02 Feb, 2019, 08:23: PM
ANSWERED BY EXPERT
