Different words are formed by arranging the letters of the word 'SUCCESS'
Q. The number of words in which C's are together but S's are separated, is

Options

A. 120
B. 96
C. 24
D. 420

Explanation

To solve the problem of finding the number of arrangements of the letters in the word "SUCCESS" where the C's are together and the S's are separated, we can follow these steps:

### Step-by-step Solution:

1. **Identify the letters in "SUCCESS":**
The word "SUCCESS" consists of the letters: S, U, C, C, E, S, S.
- Count of letters: S = 3, C = 2, U = 1, E = 1.

2. **Group the C's together:**
Since the C's must be together, we can treat "CC" as a single entity or block. This simplifies our arrangement.
- Now we have the blocks: CC, S, S, S, U, E.
- This gives us the letters: {CC, S, S, S, U, E}.

3. **Count the total letters/blocks:**
We now have 5 blocks to arrange: CC, S, S, S, U, E.

4. **Calculate the arrangements of these blocks:**
The total arrangements of these blocks can be calculated using the formula for permutations of multiset:
\[ \text{Number of arrangements} = \frac{n!}{n_1! \times n_2! \times ...} \]
Here, \( n = 6 \) (total blocks), \( n_1 = 3 \) (for S's), and \( n_2 = 1 \) (for CC, U, and E each).
\[ \text{Number of arrangements} = \frac{6!}{3! \times 1! \times 1! \times 1!} \]

5. **Calculate the factorial values:**
- \( 6! = 720 \)
- \( 3! = 6 \)
- \( 1! = 1 \)

6. **Substitute the values into the formula:**
\[ \text{Number of arrangements} = \frac{720}{6 \times 1 \times 1 \times 1} = \frac{720}{6} = 120 \]

7. **Ensure S's are separated:**
Now we need to ensure that the S's are separated. We can visualize the arrangement of the blocks (CC, U, E) first, which gives us 3 positions. We can place the S's in the gaps created by these blocks.
- The arrangement of (CC, U, E) gives us 3 gaps (before U, between U and E, and after E).
- We need to choose 3 gaps from these 3 available gaps to place the S's.

8. **Final Calculation:**
Since we have 3 gaps and we need to place 3 S's in those gaps, and they must occupy all gaps, the only arrangement is to place one S in each gap. Thus, the total arrangements remain 120.

### Final Answer:
The total number of words in which the C's are together and the S's are separated is **120**.