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In how many different ways can the letters of the word BOOKLET be arranged such that B and T always come together?
- a)360
- b)720
- c)480
- d)5040
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
In how many different ways can the letters of the word BOOKLET be arra...
Understanding the Problem
To find the number of arrangements of the letters in the word "BOOKLET" where B and T are always together, we can treat B and T as a single unit or block. This reduces the complexity of the arrangement.
Step 1: Treat B and T as a Single Block
- When B and T are together, we can represent them as one block: (BT).
- The letters of the word "BOOKLET" consist of: B, O, O, K, L, E, T.
- By treating (BT) as one letter, we now have the following letters to arrange: (BT), O, O, K, L, E.
Step 2: Count the Total Letters
- The total letters to arrange now are: (BT), O, O, K, L, E.
- This gives us a total of 6 units: (BT), O, O, K, L, E.
Step 3: Calculate Arrangements
- The formula for permutations of n objects where some objects are identical is given by: n! / (n1! * n2! * ... * nk!).
- Here, we have:
- n = 6 (total units: (BT), O, O, K, L, E).
- O appears twice (2 identical O's).
- Therefore, the number of arrangements is calculated as follows:
Number of arrangements = 6! / 2! = 720 / 2 = 360.
Step 4: Account for the Arrangement of B and T
- Within the block (BT), B and T can also be arranged in 2 ways: BT or TB.
- Therefore, the total arrangements considering B and T can be swapped are:
Total arrangements = 360 * 2 = 720.
Final Answer
Thus, the total number of arrangements of the letters in the word "BOOKLET," where B and T are always together, is 720.
The correct option is B.
To find the number of arrangements of the letters in the word "BOOKLET" where B and T are always together, we can treat B and T as a single unit or block. This reduces the complexity of the arrangement.
Step 1: Treat B and T as a Single Block
- When B and T are together, we can represent them as one block: (BT).
- The letters of the word "BOOKLET" consist of: B, O, O, K, L, E, T.
- By treating (BT) as one letter, we now have the following letters to arrange: (BT), O, O, K, L, E.
Step 2: Count the Total Letters
- The total letters to arrange now are: (BT), O, O, K, L, E.
- This gives us a total of 6 units: (BT), O, O, K, L, E.
Step 3: Calculate Arrangements
- The formula for permutations of n objects where some objects are identical is given by: n! / (n1! * n2! * ... * nk!).
- Here, we have:
- n = 6 (total units: (BT), O, O, K, L, E).
- O appears twice (2 identical O's).
- Therefore, the number of arrangements is calculated as follows:
Number of arrangements = 6! / 2! = 720 / 2 = 360.
Step 4: Account for the Arrangement of B and T
- Within the block (BT), B and T can also be arranged in 2 ways: BT or TB.
- Therefore, the total arrangements considering B and T can be swapped are:
Total arrangements = 360 * 2 = 720.
Final Answer
Thus, the total number of arrangements of the letters in the word "BOOKLET," where B and T are always together, is 720.
The correct option is B.
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In how many different ways can the letters of the word BOOKLET be arranged such that B and T always come together?a)360b)720c)480d)5040Correct answer is option 'B'. Can you explain this answer?
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In how many different ways can the letters of the word BOOKLET be arranged such that B and T always come together?a)360b)720c)480d)5040Correct answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In how many different ways can the letters of the word BOOKLET be arranged such that B and T always come together?a)360b)720c)480d)5040Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In how many different ways can the letters of the word BOOKLET be arranged such that B and T always come together?a)360b)720c)480d)5040Correct answer is option 'B'. Can you explain this answer?.
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