How many words can be formed from the letters of the word 'SERIES', which start with S and end with S?

Explanation

To solve the problem of how many words can be formed from the letters of the word "SERIES" that start with S and end with S, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Letters**: The word "SERIES" consists of the letters S, E, R, I, E, S. There are a total of 6 letters, with the letters S and E repeating.

2. **Fix the Positions**: Since we want the words to start with S and end with S, we fix S in the first and last positions. This leaves us with the letters in the middle to arrange.

3. **Count Remaining Letters**: After fixing S at the beginning and end, we have the following letters left to arrange: E, R, I, E. This gives us a total of 4 letters to arrange.

4. **Calculate Arrangements**: The number of ways to arrange these 4 letters (E, R, I, E) can be calculated using the formula for permutations of multiset:
\[ \text{Number of arrangements} = \frac{n!}{p_1! \times p_2! \times \ldots} \]
where \( n \) is the total number of items to arrange, and \( p_1, p_2, \ldots \) are the counts of each indistinguishable item.

Here, we have:
- Total letters (n) = 4 (E, R, I, E)
- E repeats 2 times.

Thus, the formula becomes:
\[ \text{Number of arrangements} = \frac{4!}{2!} \]

5. **Calculate Factorials**:
- \( 4! = 4 \times 3 \times 2 \times 1 = 24 \)
- \( 2! = 2 \times 1 = 2 \)

Now, substituting these values into the formula:
\[ \text{Number of arrangements} = \frac{24}{2} = 12 \]

6. **Final Answer**: Therefore, the total number of words that can be formed from the letters of the word "SERIES" that start with S and end with S is **12**.