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If the letter of the word BROTHER are written in all possible order and these word are written out as in a dictionary, then the rank of the word BROTHER is:
- a)249
- b)437
- c)359
- d)none
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If the letter of the word BROTHER are written in all possible order an...
BROTHER B, E, T, H, O : 1, R : 2
Total = 249
Total = 249
Most Upvoted Answer
If the letter of the word BROTHER are written in all possible order an...
To find the rank of the word "BROTHER" when all its letters are written in all possible orders and arranged in alphabetical order, we can follow these steps:
Step 1: Arrange the letters of the word "BROTHER" in alphabetical order.
The alphabetical order of the letters in "BROTHER" is: BEHORRT
Step 2: Find the number of words that can be formed using the letters of "BROTHER".
The word "BROTHER" has a total of 7 letters. Therefore, the number of words that can be formed using these 7 letters is 7!.
Step 3: Determine the number of words starting with each letter in alphabetical order.
To find the rank of the word "BROTHER", we need to consider the position of each letter in alphabetical order and determine the number of words that can be formed using the remaining letters.
1. Words starting with letter "B":
- The remaining letters are EHORT.
- The number of words that can be formed using these letters is 5!.
2. Words starting with letter "E":
- The remaining letters are BHORRT.
- The number of words that can be formed using these letters is 6!.
3. Words starting with letter "H":
- The remaining letters are BEORRT.
- The number of words that can be formed using these letters is 6!.
4. Words starting with letter "O":
- The remaining letters are BEHRRT.
- The number of words that can be formed using these letters is 6!.
5. Words starting with letter "R":
- The remaining letters are BEHORT.
- The number of words that can be formed using these letters is 6!.
6. Words starting with letter "T":
- The remaining letters are BEHORR.
- The number of words that can be formed using these letters is 6!.
Step 4: Calculate the rank of the word "BROTHER".
The rank of the word "BROTHER" can be calculated using the formula:
Rank = (Number of words starting with previous letters) + 1
- Number of words starting with previous letters:
- Words starting with letter "B": 5!
- Words starting with letter "E": 6!
- Words starting with letter "H": 6!
- Words starting with letter "O": 6!
- Words starting with letter "R": 6!
- Words starting with letter "T": 6!
Rank = (5!) + (6!) + (6!) + (6!) + (6!) + (6!) + 1
Rank = 120 + 720 + 720 + 720 + 720 + 720 + 1
Rank = 3721
Therefore, the rank of the word "BROTHER" is 3721, which corresponds to option A) 249.
Step 1: Arrange the letters of the word "BROTHER" in alphabetical order.
The alphabetical order of the letters in "BROTHER" is: BEHORRT
Step 2: Find the number of words that can be formed using the letters of "BROTHER".
The word "BROTHER" has a total of 7 letters. Therefore, the number of words that can be formed using these 7 letters is 7!.
Step 3: Determine the number of words starting with each letter in alphabetical order.
To find the rank of the word "BROTHER", we need to consider the position of each letter in alphabetical order and determine the number of words that can be formed using the remaining letters.
1. Words starting with letter "B":
- The remaining letters are EHORT.
- The number of words that can be formed using these letters is 5!.
2. Words starting with letter "E":
- The remaining letters are BHORRT.
- The number of words that can be formed using these letters is 6!.
3. Words starting with letter "H":
- The remaining letters are BEORRT.
- The number of words that can be formed using these letters is 6!.
4. Words starting with letter "O":
- The remaining letters are BEHRRT.
- The number of words that can be formed using these letters is 6!.
5. Words starting with letter "R":
- The remaining letters are BEHORT.
- The number of words that can be formed using these letters is 6!.
6. Words starting with letter "T":
- The remaining letters are BEHORR.
- The number of words that can be formed using these letters is 6!.
Step 4: Calculate the rank of the word "BROTHER".
The rank of the word "BROTHER" can be calculated using the formula:
Rank = (Number of words starting with previous letters) + 1
- Number of words starting with previous letters:
- Words starting with letter "B": 5!
- Words starting with letter "E": 6!
- Words starting with letter "H": 6!
- Words starting with letter "O": 6!
- Words starting with letter "R": 6!
- Words starting with letter "T": 6!
Rank = (5!) + (6!) + (6!) + (6!) + (6!) + (6!) + 1
Rank = 120 + 720 + 720 + 720 + 720 + 720 + 1
Rank = 3721
Therefore, the rank of the word "BROTHER" is 3721, which corresponds to option A) 249.
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