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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?
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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.
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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?
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