If the letters of the word CORONA are arranged in all possible ways and these words are written in order of a dictionary, then the word CORONA appears at the serial number

Options

A. 108
B. 110
C. 106
D. 112

Answer

To find the rank of the word "CORONA" when all its letters are arranged in alphabetical order, we can follow these steps:

### Step 1: Arrange the letters alphabetically
The letters in "CORONA" are C, O, R, O, N, A. When arranged in alphabetical order, they are:
- A, C, N, O, O, R

### Step 2: Count the total arrangements before "CORONA"
We will calculate how many words come before "CORONA" in the dictionary order.

#### Step 2.1: Words starting with 'A'
- If the first letter is 'A', the remaining letters are C, O, O, N, R.
- The number of arrangements of C, O, O, N, R is calculated as:
\[ \frac{5!}{2!} = \frac{120}{2} = 60 \]
(since 'O' is repeated twice)

#### Step 2.2: Words starting with 'C'
- If the first letter is 'C', we need to consider the second letter.
- The remaining letters are O, R, O, N, A.

##### Step 2.2.1: Words starting with 'CA'
- If the second letter is 'A', the remaining letters are O, O, R, N.
- The number of arrangements is:
\[ \frac{4!}{2!} = \frac{24}{2} = 12 \]

##### Step 2.2.2: Words starting with 'CN'
- If the second letter is 'N', the remaining letters are O, O, R, A.
- The number of arrangements is:
\[ \frac{4!}{2!} = \frac{24}{2} = 12 \]

##### Step 2.2.3: Words starting with 'CO'
- If the second letter is 'O', we need to consider the third letter.
- The remaining letters are R, O, N, A.

###### Step 2.2.3.1: Words starting with 'COA'
- If the third letter is 'A', the remaining letters are O, R, N.
- The number of arrangements is:
\[ 3! = 6 \]

###### Step 2.2.3.2: Words starting with 'COR'
- If the third letter is 'R', the remaining letters are O, O, N.
- The number of arrangements is:
\[ \frac{3!}{2!} = \frac{6}{2} = 3 \]

### Step 3: Count the arrangements leading up to "CORONA"
Now we can sum all the arrangements calculated:

- From 'A': 60
- From 'CA': 12
- From 'CN': 12
- From 'COA': 6
- From 'COR': 3

Total arrangements before "CORONA":
\[ 60 + 12 + 12 + 6 + 3 = 93 \]

### Step 4: Add 1 for the word "CORONA"
To find the rank of "CORONA", we add 1 to the total arrangements before it:
\[ 93 + 1 = 94 \]

Thus, the rank of the word "CORONA" in the dictionary order is **94**.

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