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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?
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The number of arrangements in which the letters of the word MONDAY be ...
Understanding the Problem
To find the arrangements of the letters in the word "MONDAY" that begin with M and do not end with N, we can break down the problem into manageable steps.
Step 1: Fix the First Letter
- The first letter is fixed as M.
- The remaining letters are O, N, D, A, and Y, which total 5 letters.
Step 2: Total Arrangements Without the Ending Condition
- The total arrangements of the 5 remaining letters (O, N, D, A, Y) is calculated as follows:
- Total arrangements = 5! = 120
Step 3: Arrangements Ending with N
- Now, we need to consider the arrangements that end with N.
- If N is fixed as the last letter, we are left with O, D, A, and Y.
- The total arrangements for these 4 letters (O, D, A, Y) is:
- Total arrangements = 4! = 24
Step 4: Valid Arrangements that Meet the Conditions
- To find the arrangements that begin with M and do not end with N, we subtract the arrangements ending with N from the total arrangements:
- Valid arrangements = Total arrangements - Arrangements ending with N
- Valid arrangements = 120 - 24 = 96
Conclusion
The number of arrangements of the letters in the word "MONDAY" that start with M and do not end with N is 96.
To find the arrangements of the letters in the word "MONDAY" that begin with M and do not end with N, we can break down the problem into manageable steps.
Step 1: Fix the First Letter
- The first letter is fixed as M.
- The remaining letters are O, N, D, A, and Y, which total 5 letters.
Step 2: Total Arrangements Without the Ending Condition
- The total arrangements of the 5 remaining letters (O, N, D, A, Y) is calculated as follows:
- Total arrangements = 5! = 120
Step 3: Arrangements Ending with N
- Now, we need to consider the arrangements that end with N.
- If N is fixed as the last letter, we are left with O, D, A, and Y.
- The total arrangements for these 4 letters (O, D, A, Y) is:
- Total arrangements = 4! = 24
Step 4: Valid Arrangements that Meet the Conditions
- To find the arrangements that begin with M and do not end with N, we subtract the arrangements ending with N from the total arrangements:
- Valid arrangements = Total arrangements - Arrangements ending with N
- Valid arrangements = 120 - 24 = 96
Conclusion
The number of arrangements of the letters in the word "MONDAY" that start with M and do not end with N is 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?
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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? 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? 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?.
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? 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? 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?.
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