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

Answer

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

### Step 1: Identify the total number of letters
The word "INDIA" consists of 5 letters: I, N, D, I, A.

### Step 2: Count the total letters and identify repetitions
In the word "INDIA":
- Total letters = 5
- The letter 'I' repeats 2 times.

### Step 3: Use the formula for permutations of multiset
The formula for the number of permutations of a word where certain letters are repeated is given by:

\[ \text{Number of permutations} = \frac{n!}{r_1! \times r_2! \times \ldots \times r_k!} \]

Where:
- \( n \) is the total number of letters,
- \( r_1, r_2, \ldots, r_k \) are the frequencies of the repeated letters.

In our case:
- \( n = 5 \) (total letters),
- The letter 'I' appears 2 times, so \( r_1 = 2 \).

### Step 4: Substitute values into the formula
Now, we can substitute the values into the formula:

\[ \text{Number of permutations} = \frac{5!}{2!} \]

### Step 5: Calculate the factorials
Now we calculate the factorials:
- \( 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \)
- \( 2! = 2 \times 1 = 2 \)

### Step 6: Perform the division
Now we divide \( 5! \) by \( 2! \):

\[ \text{Number of permutations} = \frac{120}{2} = 60 \]

### Conclusion
Thus, the number of permutations of the letters in the word "INDIA" is **60**.

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