The total number of different combinations of letters which can be made from the letters of the word MISSISSIPPI, is

Options

A. 150
B. 148
C. 149
D. none of these

Answer

To find the total number of different combinations of letters that can be made from the letters of the word "MISSISSIPPI", we can follow these steps:

### Step 1: Count the total letters and their frequencies
The word "MISSISSIPPI" consists of 11 letters in total. The breakdown of the letters is as follows:
- M: 1
- I: 4
- S: 4
- P: 2

### Step 2: Use the formula for combinations of multiset
The formula for the number of distinct permutations of a multiset is given by:

\[ \text{Total combinations} = \frac{n!}{n_1! \times n_2! \times n_3! \times \ldots} \]

where:
- \( n \) is the total number of items,
- \( n_1, n_2, n_3, \ldots \) are the frequencies of the distinct items.

In our case:
- Total letters \( n = 11 \)
- Frequencies: \( n_1 = 1 \) (for M), \( n_2 = 4 \) (for I), \( n_3 = 4 \) (for S), \( n_4 = 2 \) (for P)

### Step 3: Calculate the factorials
Now we can substitute these values into the formula:

\[ \text{Total combinations} = \frac{11!}{1! \times 4! \times 4! \times 2!} \]

Calculating the factorials:
- \( 11! = 39916800 \)
- \( 1! = 1 \)
- \( 4! = 24 \)
- \( 2! = 2 \)

### Step 4: Substitute and simplify
Now we can substitute these values into our equation:

\[ \text{Total combinations} = \frac{39916800}{1 \times 24 \times 24 \times 2} \]

Calculating the denominator:

\[ 1 \times 24 \times 24 \times 2 = 1152 \]

Now, we can compute:

\[ \text{Total combinations} = \frac{39916800}{1152} = 34650 \]

### Step 5: Exclude the empty combination
Since we need to find the total number of different combinations of letters (not including the empty combination), we subtract 1 from our total:

\[ \text{Final combinations} = 34650 - 1 = 34649 \]

Thus, the total number of different combinations of letters that can be made from the letters of the word "MISSISSIPPI" is **34649**.