Find the number of permutations of the letter of the words
'CHANDIGARH'

Answer

To find the number of permutations of the letters in the word "CHANDIGARH", we will follow these steps:

### Step 1: Count the Total Letters
The word "CHANDIGARH" consists of 10 letters.

### Step 2: Identify the Repeated Letters
Next, we need to identify any letters that are repeated in the word:
- C: 1
- H: 2 (there are two H's)
- A: 2 (there are two A's)
- N: 1
- D: 1
- I: 1
- G: 1
- R: 1

### Step 3: Apply the Permutation Formula
The formula for permutations of a multiset is given by:

\[ \text{Number of permutations} = \frac{n!}{p_1! \times p_2! \times \ldots \times p_k!} \]

where:
- \( n \) is the total number of items,
- \( p_1, p_2, \ldots, p_k \) are the frequencies of the repeated items.

In our case:
- \( n = 10 \) (total letters)
- The repeated letters are H (2) and A (2).

Thus, we can substitute into the formula:

\[ \text{Number of permutations} = \frac{10!}{2! \times 2!} \]

### Step 4: Calculate Factorials
Now, we will calculate the factorials:
- \( 10! = 3628800 \)
- \( 2! = 2 \)

### Step 5: Substitute and Calculate
Substituting the values into the formula gives:

\[ \text{Number of permutations} = \frac{3628800}{2 \times 2} = \frac{3628800}{4} = 907200 \]

### Final Answer
The total number of permutations of the letters in the word "CHANDIGARH" is **907200**.

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