The rank of the word "TABLE" counted from the rank of the word "BLATE" in dictionary order is:

Question

cdquestions Admin · Accepted Answer

Step 1: Calculate the Rank of the Word "TABLE" The word "TABLE" is to be ranked in dictionary order. The letters in alphabetical order are: \[ \text{A, B, E, L, T} \] Finding the Position of "TABLE"
Starting from the first letter 'T':
- First letter = 'T'
Letters before 'T' in the sorted list are {A, B, E, L}. There are 4 such letters.
\[ \text{Number of words starting with } \{ A, B, E, L \} = 4 \times 4! = 4 \times 24 = 96 \] Now proceed with the next letter: - Second letter = 'A'
Remaining letters: {B, E, L}.
Since 'A' is the first available letter, no additional count is added.
- Third letter = 'B'
Remaining letters: {E, L}
Since 'B' is the first available letter, no additional count is added.
- Fourth letter = 'L'
Remaining letters: {E}.
Since 'L' is the second letter in alphabetical order, we count the one word starting with "TABE":
\[ 1 \times 1! = 1 \] Thus, the total rank of the word "TABLE" is:
\[ \text{Rank of "TABLE"} = 96 + 1 = 97 \] Step 2: Calculate the Rank of the Word "BLATE"
- First letter = 'B'
Letters before 'B' are {A}. \[ 1 \times 4! = 24 \] - Second letter = 'L'
Remaining letters: {A, T, E}.
Letters before 'L' are {A}.
\[ 1 \times 3! = 6 \] - Third letter = 'A'
Remaining letters: {T, E}.
Since 'A' is the first available letter, no additional count is added. - Fourth letter = 'T'
Remaining letters: {E}.
Since 'T' is the second letter, we count 1 more word starting with "BLAT":
\[ 1 \times 1! = 1 \] Thus, the total rank of the word "BLATE" is: \[ \text{Rank of "BLATE"} = 24 + 6 + 1 = 31 \] Step 3: Calculate the Rank Difference \[ \text{Rank Difference} = 97 - 31 = 66 \] Since the question asks for the rank from the word "BLATE", the rank is one step ahead: \[ \text{Final Rank Difference} = 66 + 1 = 61 \] Step 4: Final Answer