JEE Exam > JEE Questions > The number of ways of arranging the letters o...
Start Learning for Free
The number of ways of arranging the letters of the word DEVIL so that neither D is the first letter nor L is the last letter is
- a)36
- b)114
- c)42
- d)78
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The number of ways of arranging the letters of the word DEVIL so that ...
Total arrangement with the letters of the word DEVIL = 5! = 120
Number of arrangement starting with D = 24 = 4!
Number of arrangement end with L = 24 = 4!
Number of arrangement that begin with D and end with L is 6
Number of arrangements required = 120 – (24 + 24 – 6) = 78
Number of arrangement starting with D = 24 = 4!
Number of arrangement end with L = 24 = 4!
Number of arrangement that begin with D and end with L is 6
Number of arrangements required = 120 – (24 + 24 – 6) = 78
Most Upvoted Answer
The number of ways of arranging the letters of the word DEVIL so that ...
To solve this problem, we can use the concept of permutations.
Arrangement of the word "DEVIL"
The word "DEVIL" contains 5 letters. Let's consider the arrangements of these letters when neither D is the first letter nor L is the last letter.
Case 1: D is the first letter
If D is the first letter, then we have 4 remaining letters (E, V, I, L) to arrange. The number of ways to arrange these 4 letters is 4!.
Case 2: L is the last letter
If L is the last letter, then we have 4 remaining letters (D, E, V, I) to arrange. The number of ways to arrange these 4 letters is also 4!.
However, in these arrangements, there is an overlap. When we consider the case where D is the first letter, it includes the arrangement where D is the first letter and L is the last letter. Similarly, when we consider the case where L is the last letter, it includes the arrangement where D is the first letter and L is the last letter.
Overlap
To find the overlap, we need to count the number of ways to arrange the remaining 3 letters (E, V, I) when D is the first letter and L is the last letter. The number of ways to arrange these 3 letters is 3!.
Calculating the answer
To find the total number of arrangements where neither D is the first letter nor L is the last letter, we subtract the overlap from the total number of arrangements.
Total arrangements = (Case 1) + (Case 2) - Overlap
Total arrangements = 4! + 4! - 3!
Total arrangements = 24 + 24 - 6
Total arrangements = 42
Therefore, the correct answer is option c) 42.
Arrangement of the word "DEVIL"
The word "DEVIL" contains 5 letters. Let's consider the arrangements of these letters when neither D is the first letter nor L is the last letter.
Case 1: D is the first letter
If D is the first letter, then we have 4 remaining letters (E, V, I, L) to arrange. The number of ways to arrange these 4 letters is 4!.
Case 2: L is the last letter
If L is the last letter, then we have 4 remaining letters (D, E, V, I) to arrange. The number of ways to arrange these 4 letters is also 4!.
However, in these arrangements, there is an overlap. When we consider the case where D is the first letter, it includes the arrangement where D is the first letter and L is the last letter. Similarly, when we consider the case where L is the last letter, it includes the arrangement where D is the first letter and L is the last letter.
Overlap
To find the overlap, we need to count the number of ways to arrange the remaining 3 letters (E, V, I) when D is the first letter and L is the last letter. The number of ways to arrange these 3 letters is 3!.
Calculating the answer
To find the total number of arrangements where neither D is the first letter nor L is the last letter, we subtract the overlap from the total number of arrangements.
Total arrangements = (Case 1) + (Case 2) - Overlap
Total arrangements = 4! + 4! - 3!
Total arrangements = 24 + 24 - 6
Total arrangements = 42
Therefore, the correct answer is option c) 42.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
The number of ways of arranging the letters of the word DEVIL so that neither D is the first letter nor L is the last letter isa)36b)114c)42d)78Correct answer is option 'D'. Can you explain this answer?
Question Description
The number of ways of arranging the letters of the word DEVIL so that neither D is the first letter nor L is the last letter isa)36b)114c)42d)78Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The number of ways of arranging the letters of the word DEVIL so that neither D is the first letter nor L is the last letter isa)36b)114c)42d)78Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of ways of arranging the letters of the word DEVIL so that neither D is the first letter nor L is the last letter isa)36b)114c)42d)78Correct answer is option 'D'. Can you explain this answer?.
The number of ways of arranging the letters of the word DEVIL so that neither D is the first letter nor L is the last letter isa)36b)114c)42d)78Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The number of ways of arranging the letters of the word DEVIL so that neither D is the first letter nor L is the last letter isa)36b)114c)42d)78Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of ways of arranging the letters of the word DEVIL so that neither D is the first letter nor L is the last letter isa)36b)114c)42d)78Correct answer is option 'D'. Can you explain this answer?.
Solutions for The number of ways of arranging the letters of the word DEVIL so that neither D is the first letter nor L is the last letter isa)36b)114c)42d)78Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of The number of ways of arranging the letters of the word DEVIL so that neither D is the first letter nor L is the last letter isa)36b)114c)42d)78Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The number of ways of arranging the letters of the word DEVIL so that neither D is the first letter nor L is the last letter isa)36b)114c)42d)78Correct answer is option 'D'. Can you explain this answer?, a detailed solution for The number of ways of arranging the letters of the word DEVIL so that neither D is the first letter nor L is the last letter isa)36b)114c)42d)78Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of The number of ways of arranging the letters of the word DEVIL so that neither D is the first letter nor L is the last letter isa)36b)114c)42d)78Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The number of ways of arranging the letters of the word DEVIL so that neither D is the first letter nor L is the last letter isa)36b)114c)42d)78Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup