CA Foundation Exam > CA Foundation Questions > The number of arrangements in which the lette...
Start Learning for Free
The number of arrangements in which the letters of the word MONDAY be arranged so that the words thus formed begin with M and do not end with N is
- a)720
- b)120
- c)96
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The number of arrangements in which the letters of the word MONDAY be ...
No. of choice for 1st letter : 1 (M)
No. of choice for last letter : 4 (≠N,M)
for 2,3,4,5 letters no. of choices : 4,3,2,1
Total words : 1x4x4x3x2x1 = 96 words
Most Upvoted Answer
The number of arrangements in which the letters of the word MONDAY be ...
Given: The word MONDAY
To find: Number of arrangements in which the words formed begin with M and do not end with N
Solution:
There are 6 letters in the word MONDAY
To form a word starting with M, we fix the first letter as M
So, we have to arrange the remaining 5 letters (O, N, D, A, Y) in such a way that the word does not end with N
Let's consider the cases where the word ends with N and subtract it from the total number of arrangements
Case 1: Word ends with N
If the word ends with N, then M _ _ _ _ N
The remaining 4 letters can be arranged in 4! ways
Total number of arrangements = 1 × 4! = 24
Case 2: Word does not end with N
If the word does not end with N, then M _ _ _ _ _ (the last letter can be any of the remaining 4 letters)
The last letter can be filled in 4 ways (since we can't use N)
The remaining 4 letters can be arranged in 4! ways
Total number of arrangements = 4 × 4! = 96
Therefore, the required number of arrangements = Total number of arrangements - Number of arrangements where the word ends with N
= 120 - 24 = 96
Hence, the correct option is (c) 96.
To find: Number of arrangements in which the words formed begin with M and do not end with N
Solution:
There are 6 letters in the word MONDAY
To form a word starting with M, we fix the first letter as M
So, we have to arrange the remaining 5 letters (O, N, D, A, Y) in such a way that the word does not end with N
Let's consider the cases where the word ends with N and subtract it from the total number of arrangements
Case 1: Word ends with N
If the word ends with N, then M _ _ _ _ N
The remaining 4 letters can be arranged in 4! ways
Total number of arrangements = 1 × 4! = 24
Case 2: Word does not end with N
If the word does not end with N, then M _ _ _ _ _ (the last letter can be any of the remaining 4 letters)
The last letter can be filled in 4 ways (since we can't use N)
The remaining 4 letters can be arranged in 4! ways
Total number of arrangements = 4 × 4! = 96
Therefore, the required number of arrangements = Total number of arrangements - Number of arrangements where the word ends with N
= 120 - 24 = 96
Hence, the correct option is (c) 96.
Free Test
FREE
| Start Free Test |
Community Answer
The number of arrangements in which the letters of the word MONDAY be ...
Step 1: Total number of letters in "MONDAY"
The word "MONDAY" has 6 distinct letters: M, O, N, D, A, Y.
The word "MONDAY" has 6 distinct letters: M, O, N, D, A, Y.
Step 2: Fixing the first letter as 'M'
Since the word must begin with 'M', we can fix 'M' in the first position. Now we are left with 5 positions to arrange the remaining letters: O, N, D, A, Y.
Since the word must begin with 'M', we can fix 'M' in the first position. Now we are left with 5 positions to arrange the remaining letters: O, N, D, A, Y.
Step 3: Calculate the number of arrangements without any restriction
If there were no restriction on the last letter, we would arrange the remaining 5 letters (O, N, D, A, Y) in the remaining 5 positions. The number of ways to do this is:
5! = 5 × 4 × 3 × 2 × 1 = 120
If there were no restriction on the last letter, we would arrange the remaining 5 letters (O, N, D, A, Y) in the remaining 5 positions. The number of ways to do this is:
5! = 5 × 4 × 3 × 2 × 1 = 120
Step 4: Subtract the cases where the word ends with 'N'
Now, we need to subtract the cases where the word ends with 'N'. If 'N' is at the last position, we are left with arranging the remaining 4 letters: O, D, A, Y.
The number of ways to arrange these 4 letters is:
4! = 4 × 3 × 2 × 1 = 24
Now, we need to subtract the cases where the word ends with 'N'. If 'N' is at the last position, we are left with arranging the remaining 4 letters: O, D, A, Y.
The number of ways to arrange these 4 letters is:
4! = 4 × 3 × 2 × 1 = 24
Step 5: Calculate the total number of valid arrangements
The total number of arrangements where the word starts with 'M' and does not end with 'N' is:
5! - 4! = 120 - 24 = 96
The total number of arrangements where the word starts with 'M' and does not end with 'N' is:
5! - 4! = 120 - 24 = 96
Final Answer:
The number of arrangements in which the letters of the word "MONDAY" can be arranged such that the word begins with 'M' and does not end with 'N' is 96.
The number of arrangements in which the letters of the word "MONDAY" can be arranged such that the word begins with 'M' and does not end with 'N' is 96.
Attention CA Foundation Students!
To make sure you are not studying endlessly, EduRev has designed CA Foundation study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CA Foundation.
|
Explore Courses for CA Foundation exam
|
|
Similar CA Foundation Doubts
Top Courses for CA FoundationView all
The number of arrangements in which the letters of the word MONDAY be arranged so that the words thus formed begin with M and do not end with N isa)720b)120c)96d)none of theseCorrect answer is option 'C'. Can you explain this answer?
Question Description
The number of arrangements in which the letters of the word MONDAY be arranged so that the words thus formed begin with M and do not end with N isa)720b)120c)96d)none of theseCorrect answer is option 'C'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The number of arrangements in which the letters of the word MONDAY be arranged so that the words thus formed begin with M and do not end with N isa)720b)120c)96d)none of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of arrangements in which the letters of the word MONDAY be arranged so that the words thus formed begin with M and do not end with N isa)720b)120c)96d)none of theseCorrect answer is option 'C'. Can you explain this answer?.
The number of arrangements in which the letters of the word MONDAY be arranged so that the words thus formed begin with M and do not end with N isa)720b)120c)96d)none of theseCorrect answer is option 'C'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The number of arrangements in which the letters of the word MONDAY be arranged so that the words thus formed begin with M and do not end with N isa)720b)120c)96d)none of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of arrangements in which the letters of the word MONDAY be arranged so that the words thus formed begin with M and do not end with N isa)720b)120c)96d)none of theseCorrect answer is option 'C'. Can you explain this answer?.
Solutions for The number of arrangements in which the letters of the word MONDAY be arranged so that the words thus formed begin with M and do not end with N isa)720b)120c)96d)none of theseCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for CA Foundation.
Download more important topics, notes, lectures and mock test series for CA Foundation Exam by signing up for free.
Here you can find the meaning of The number of arrangements in which the letters of the word MONDAY be arranged so that the words thus formed begin with M and do not end with N isa)720b)120c)96d)none of theseCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The number of arrangements in which the letters of the word MONDAY be arranged so that the words thus formed begin with M and do not end with N isa)720b)120c)96d)none of theseCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for The number of arrangements in which the letters of the word MONDAY be arranged so that the words thus formed begin with M and do not end with N isa)720b)120c)96d)none of theseCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of The number of arrangements in which the letters of the word MONDAY be arranged so that the words thus formed begin with M and do not end with N isa)720b)120c)96d)none of theseCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The number of arrangements in which the letters of the word MONDAY be arranged so that the words thus formed begin with M and do not end with N isa)720b)120c)96d)none of theseCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice CA Foundation tests.
|
|
Explore Courses for CA Foundation exam
|
|
Suggested Free Tests
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