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The number of arrangements of the letters of the word BANANA in which the two N’s do not appear adjacently is _____________.
Correct answer is '40'. Can you explain this answer?
Verified Answer
The number of arrangements of the letters of the word BANANA in which ...
In BANANA. Letter A reapets 3 times and N reapets 2 times.
Total number of arrangements of word BANANA is
Let both N s are appear together, then they are considered is single letter.
In this way total number of arrangements are
Hence total number of arrangements where N do not appear adjacently is = 60 - 20 = 40
Total number of arrangements of word BANANA is
Let both N s are appear together, then they are considered is single letter.
In this way total number of arrangements are
Hence total number of arrangements where N do not appear adjacently is = 60 - 20 = 40
Most Upvoted Answer
The number of arrangements of the letters of the word BANANA in which ...
We can start by considering the total number of arrangements of the letters in BANANA, which is 6! (since there are 6 letters in total). However, this counts all arrangements, including those where the two N's are not together.
To eliminate these arrangements, we can treat the two N's as a single "letter" and consider the number of arrangements of the resulting 5 "letters" (B, A, N, A, A). This gives us 5! arrangements.
However, we have overcounted the arrangements where the two A's are indistinguishable. Specifically, for each arrangement where the two A's are swapped, we have counted it twice. There are 2! = 2 ways to swap the A's, so we need to divide our count by 2 to correct for this.
Therefore, the final answer is:
5!/2 = 60/2 = 30 arrangements.
To eliminate these arrangements, we can treat the two N's as a single "letter" and consider the number of arrangements of the resulting 5 "letters" (B, A, N, A, A). This gives us 5! arrangements.
However, we have overcounted the arrangements where the two A's are indistinguishable. Specifically, for each arrangement where the two A's are swapped, we have counted it twice. There are 2! = 2 ways to swap the A's, so we need to divide our count by 2 to correct for this.
Therefore, the final answer is:
5!/2 = 60/2 = 30 arrangements.
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The number of arrangements of the letters of the word BANANA in which the two N’s do not appear adjacently is _____________.Correct answer is '40'. Can you explain this answer? for IIT JAM 2025 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about The number of arrangements of the letters of the word BANANA in which the two N’s do not appear adjacently is _____________.Correct answer is '40'. Can you explain this answer? covers all topics & solutions for IIT JAM 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of arrangements of the letters of the word BANANA in which the two N’s do not appear adjacently is _____________.Correct answer is '40'. Can you explain this answer?.
The number of arrangements of the letters of the word BANANA in which the two N’s do not appear adjacently is _____________.Correct answer is '40'. Can you explain this answer? for IIT JAM 2025 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about The number of arrangements of the letters of the word BANANA in which the two N’s do not appear adjacently is _____________.Correct answer is '40'. Can you explain this answer? covers all topics & solutions for IIT JAM 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of arrangements of the letters of the word BANANA in which the two N’s do not appear adjacently is _____________.Correct answer is '40'. Can you explain this answer?.
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