Question

The letters of the word "COCHIN" are permuted and all the permutations are arranged in alphabetical order as in an English dictionary. The number of words that appear before the word "COCHIN" is

• A. 48
• B. 96
• C. 192
• D. 360

Hint:

When dealing with permutations of words, always first list the letters in alphabetical order and then calculate the number of words that start with each letter that is less than the starting letter of the given word.

Answer 1

The Correct Option is B

The given word is "COCHIN". We need to find how many words appear before "COCHIN" when all permutations of the letters are arranged in alphabetical order. 
The letters of the word "COCHIN" in alphabetical order are: \( C, C, H, I, N, O \). 1. First letter: The first letter in "COCHIN" is \( C \), and the words starting with \( A \) and \( B \) will precede it. 
Since there are no \( A \)'s or \( B \)'s in the word, we move to the next letter. 2. Second letter: The second letter in "COCHIN" is \( O \). So, we will find all permutations where the first letter is \( C \), but the second letter is less than \( O \). - If the second letter is \( C \), the possible remaining letters are: \( H, I, N, O \). The number of permutations of these 4 letters is: \[ P(4) = 4! = 24 \] 3. Third letter: The third letter in "COCHIN" is \( H \). Now, we find the permutations where the first two letters are \( C \) and \( O \), but the third letter is less than \( H \). - If the third letter is \( I \), the remaining letters are \( H, N \), so the number of permutations of these two letters is: \[ P(2) = 2! = 2 \] Thus, the total number of permutations that appear before "COCHIN" is: \[ 24 + 2 = 96 \]