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How many arrangements of the letters A, C, C, E, N, T include at least one letter between the two C’s?
- a)60
- b)120
- c)240
- d)360
- e)720
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
How many arrangements of the letters A, C, C, E, N, T include at least...
Understanding the Problem
We need to find the number of arrangements of the letters in the word "ACCENT" where at least one letter is placed between the two C's.
Total Arrangements Without Restrictions
- The word "ACCENT" has 6 letters: A, C, C, E, N, T.
- The total arrangements can be calculated using the formula for permutations of multiset:
Total = 6! / (2!) = 720 / 2 = 360 arrangements.
Arrangements With C's Together
- Now, we calculate the arrangements where the two C's are together.
- We can treat the pair "CC" as a single unit/block. The new arrangement will be "CC, A, E, N, T" which consists of 5 units.
Total = 5! = 120 arrangements.
Finding Arrangements With At Least One Letter Between C's
- To find the arrangements where at least one letter is between the C's, we subtract the arrangements where the C's are together from the total arrangements.
Required arrangements = Total arrangements - Arrangements with C's together
Required arrangements = 360 - 120 = 240.
Conclusion
Thus, the number of arrangements of the letters A, C, C, E, N, T that include at least one letter between the two C's is 240.
Therefore, the correct answer is option 'C'.
We need to find the number of arrangements of the letters in the word "ACCENT" where at least one letter is placed between the two C's.
Total Arrangements Without Restrictions
- The word "ACCENT" has 6 letters: A, C, C, E, N, T.
- The total arrangements can be calculated using the formula for permutations of multiset:
Total = 6! / (2!) = 720 / 2 = 360 arrangements.
Arrangements With C's Together
- Now, we calculate the arrangements where the two C's are together.
- We can treat the pair "CC" as a single unit/block. The new arrangement will be "CC, A, E, N, T" which consists of 5 units.
Total = 5! = 120 arrangements.
Finding Arrangements With At Least One Letter Between C's
- To find the arrangements where at least one letter is between the C's, we subtract the arrangements where the C's are together from the total arrangements.
Required arrangements = Total arrangements - Arrangements with C's together
Required arrangements = 360 - 120 = 240.
Conclusion
Thus, the number of arrangements of the letters A, C, C, E, N, T that include at least one letter between the two C's is 240.
Therefore, the correct answer is option 'C'.
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How many arrangements of the letters A, C, C, E, N, T include at least one letter between the two C’s?a)60b)120c)240d)360e)720Correct answer is option 'C'. Can you explain this answer?
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How many arrangements of the letters A, C, C, E, N, T include at least one letter between the two C’s?a)60b)120c)240d)360e)720Correct answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about How many arrangements of the letters A, C, C, E, N, T include at least one letter between the two C’s?a)60b)120c)240d)360e)720Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many arrangements of the letters A, C, C, E, N, T include at least one letter between the two C’s?a)60b)120c)240d)360e)720Correct answer is option 'C'. Can you explain this answer?.
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