Find the number of words formed with the letters of the word 'MISSISSIPPI'.

Answer

To find the number of distinct words that can be formed from the letters of the word "MISSISSIPPI", we can follow these steps:

### Step 1: Count the total letters
The word "MISSISSIPPI" consists of 11 letters in total.

### Step 2: Identify the frequency of each letter
In the word "MISSISSIPPI", the frequency of each letter is as follows:
- M: 1
- I: 5
- S: 4
- P: 2

### Step 3: Use the formula for permutations of multiset
The formula for the number of distinct permutations of a multiset is given by:

\[ \text{Number of permutations} = \frac{n!}{n_1! \times n_2! \times n_3! \times \ldots} \]

Where:
- \( n \) is the total number of items (letters in this case),
- \( n_1, n_2, n_3, \ldots \) are the frequencies of the distinct items.

### Step 4: Apply the formula
Here, \( n = 11 \) (total letters), \( n_1 = 1 \) (for M), \( n_2 = 5 \) (for I), \( n_3 = 4 \) (for S), and \( n_4 = 2 \) (for P). Thus, we have:

\[ \text{Number of permutations} = \frac{11!}{1! \times 5! \times 4! \times 2!} \]

### Step 5: Calculate the factorials
Now, we need to calculate the factorial values:
- \( 11! = 39916800 \)
- \( 1! = 1 \)
- \( 5! = 120 \)
- \( 4! = 24 \)
- \( 2! = 2 \)

### Step 6: Substitute the values into the formula
Now substituting these values into the formula:

\[ \text{Number of permutations} = \frac{39916800}{1 \times 120 \times 24 \times 2} \]

### Step 7: Calculate the denominator
Calculating the denominator:

\[ 1 \times 120 \times 24 \times 2 = 5760 \]

### Step 8: Final calculation
Now we can calculate the final number of permutations:

\[ \text{Number of permutations} = \frac{39916800}{5760} = 6930 \]

### Conclusion
Thus, the total number of distinct words that can be formed with the letters of the word "MISSISSIPPI" is **6930**.

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