How many words can be formed with the letters of the words 'TRIANGLE', if each word starts with R and ends with E?

Answer

To solve the problem of how many words can be formed with the letters of the word "TRIANGLE" starting with 'R' and ending with 'E', we can follow these steps:

### Step-by-Step Solution:

1. **Identify the total letters in "TRIANGLE":**
The word "TRIANGLE" consists of 8 letters: T, R, I, A, N, G, L, E.

2. **Fix the first and last letters:**
According to the problem, the first letter must be 'R' and the last letter must be 'E'. Therefore, we can represent the arrangement as:
\[ R \_ \_ \_ \_ \_ \_ E \]
This means we have fixed 2 letters (R and E) in their respective positions.

3. **Count the remaining letters:**
After fixing 'R' and 'E', we are left with the letters T, I, A, N, G, and L. This gives us a total of 6 letters to arrange.

4. **Calculate the arrangements of the remaining letters:**
The number of ways to arrange these 6 letters is given by the factorial of the number of letters. Therefore, we need to calculate \(6!\):
\[ 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 \]

5. **Conclusion:**
The total number of words that can be formed with the letters of "TRIANGLE" starting with 'R' and ending with 'E' is 720.

### Final Answer:
The total number of words that can be formed is **720**.