The letters of the word “COCHIN” are permuted and all the permutations are arranged in alphabetical order as in the English dictionary. The number of words that appear before the word ‘COCHIN’ is:

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answer is C.

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Detailed Solution

We are given with the word COCHIN
Let us arrange each letter in the order of alphabets then we get
C, C, H, I, N, O
Here, we can see that there are six letters
Let us assume that there are six boxes in which the letters need to be arranged as follows

Now, let us place the first letter C in the first box then we get

Here, we can see that the first letter of COCHIN and the first letter of our arrangement is the same.
So we can say that the first box is fixed with letter C
Now, let us place the second letter C in the second box then we get

Here, we can see that the second letter is not matching with COCHIN
So, let us arrange the remaining 4 letters in four other boxes.
We know that the condition that number of ways of arranging n objects is given as n!
By using the above condition we get number of ways of arranging 4 letters is 4!
Now, let us place the next letter that is H in the second box then we get

Here, we can see that the second letter is not matching with COCHIN
So, let us arrange the remaining 4 letters in four other boxes.
By using the condition of the arrangement we get number of ways of arranging 4 letters is 4!
Here, we can see that the total number of arrangements until now as
⇒ 4! + 4! = 24 + 24
⇒4! + 4! = 48
Now, let us place the next letter that is I in the second box then we get

Here, we can see that the second letter is not matching with COCHIN
So, let us arrange the remaining 4 letters in the other four boxes.
By using the condition of the arrangement we get the number of ways of arranging 4 letters is 4!
Here, we can see that the total number of arrangements until now as
⇒ 48 + 4! = 48 + 24 = 72
Now, let us place the next letter that is N in the second box then we get

Here, we can see that the second letter is not matching with COCHIN
So, let us arrange the remaining 4 letters in the other four boxes.
By using the condition of the arrangement we get the number of ways of arranging 4 letters is 4!
Here, we can see that the total number of arrangements until now as
⇒72 + 4! = 72 + 24 = 96
Now, let us place the next letter that is O in the second box then we get

Here, we can see that the second letter in COCHIN is matching with our permutations
So, we can fix the two letters in the first two boxes
Now, let us place the first letter from the remaining letters that is C in the third box then we get

Here, we can see that the third letter in COCHIN is matching with our permutations
So, we can fix the three letters in the first three boxes
Now, let us place the first letter from the remaining letters that is H, I, and N the remaining boxes respectively then we get

Here, we can see that there are a total of 96 words before the word COCHIN.

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