The number of ways in which four S come consecutively in the word MISSISSIPPI, is

Options

A. 420
B. 840
C. 210
D. 630

Explanation

To solve the problem of finding the number of ways in which four S's come consecutively in the word "MISSISSIPPI", we can follow these steps:

### Step 1: Identify the letters in the word
The word "MISSISSIPPI" consists of the following letters:
- M: 1
- I: 4
- S: 4
- P: 2

### Step 2: Group the four S's together
Since we want the four S's to be consecutive, we can treat them as a single unit or letter. Therefore, we can represent the four S's as one block, which we will call "S4".

### Step 3: Count the total letters after grouping
After grouping the four S's, we have the following letters:
- S4 (the block of four S's)
- M (1)
- I (4)
- P (2)

This gives us a total of:
- S4, M, I, I, I, I, P, P

So, we have 8 units in total:
- S4, M, I, I, I, I, P, P

### Step 4: Calculate the arrangements of these letters
Now, we need to find the number of arrangements of these 8 units. The formula for arrangements of n items where there are repetitions is given by:

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

Where:
- \( n \) is the total number of items,
- \( n_1, n_2, \ldots, n_k \) are the frequencies of the repeated items.

In our case:
- Total letters (n) = 8
- I appears 4 times,
- P appears 2 times.

Thus, the number of arrangements is:

\[ \text{Number of arrangements} = \frac{8!}{4! \times 2!} \]

### Step 5: Calculate the factorials
Now, we calculate the factorials:
- \( 8! = 40320 \)
- \( 4! = 24 \)
- \( 2! = 2 \)

Substituting these values into the formula gives:

\[ \text{Number of arrangements} = \frac{40320}{24 \times 2} = \frac{40320}{48} = 840 \]

### Step 6: Consider the arrangement of the S's
Since the four S's are identical, there is only 1 way to arrange them within their block.

### Final Answer
The total number of ways in which four S's can come consecutively in the word "MISSISSIPPI" is **840**.

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