Different words are formed by arranging the letters of the word `SUC CESS`, then find the total possible words .

Options

A. 42
B. 40
C. 420
D. 480

Explanation

To find the total number of different words that can be formed by arranging the letters of the word "SUCCESS", we will follow these steps:

### Step 1: Count the total number of letters
The word "SUCCESS" consists of the following letters: S, U, C, C, E, S, S.
Counting these letters, we have:
- S: 3 times
- U: 1 time
- C: 2 times
- E: 1 time

Thus, the total number of letters is 7.

### Step 2: Identify the repeating letters
In the word "SUCCESS":
- The letter S appears 3 times.
- The letter C appears 2 times.
- The letter U and E appear 1 time each.

### Step 3: Apply the formula for permutations of multiset
The formula for finding the number of distinct arrangements of letters in a word where some letters are repeated is given by:

\[ \text{Total arrangements} = \frac{n!}{p_1! \times p_2! \times \ldots \times p_k!} \]

where:
- \( n \) is the total number of letters,
- \( p_1, p_2, \ldots, p_k \) are the frequencies of the repeating letters.

In our case:
- \( n = 7 \) (total letters)
- The frequencies are: S (3), C (2), U (1), E (1).

Thus, we will use:
\[ \text{Total arrangements} = \frac{7!}{3! \times 2! \times 1! \times 1!} \]

### Step 4: Calculate the factorials
Now, we calculate the factorials:
- \( 7! = 5040 \)
- \( 3! = 6 \)
- \( 2! = 2 \)
- \( 1! = 1 \)

### Step 5: Substitute and simplify
Now substituting these values into the formula:
\[ \text{Total arrangements} = \frac{5040}{6 \times 2 \times 1 \times 1} = \frac{5040}{12} = 420 \]

### Final Answer
Thus, the total number of different words that can be formed by arranging the letters of the word "SUCCESS" is **420**.

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