how many words begin with R and ends with W , in RAINBOW word.

Options

A. a. 120
B. b. 240
C. c. 180
D. d. 360

Answer

To solve the problem of how many words can be formed from the letters of the word "RAINBOW" that begin with 'R' and end with 'W', we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Fixed Letters**:
- The first letter must be 'R' and the last letter must be 'W'.
- Thus, we have: R _ _ _ _ W.

2. **Count the Remaining Letters**:
- The word "RAINBOW" consists of 7 letters: R, A, I, N, B, O, W.
- Since 'R' and 'W' are already used, we are left with the letters: A, I, N, B, O.
- This gives us a total of 5 letters to arrange.

3. **Calculate the Arrangements**:
- The number of ways to arrange 5 letters is given by the factorial of the number of letters, which is 5!.
- Therefore, we need to calculate 5! (5 factorial).

4. **Calculate 5!**:
- 5! = 5 × 4 × 3 × 2 × 1 = 120.

5. **Conclusion**:
- Thus, the total number of words that can be formed starting with 'R' and ending with 'W' is 120.

### Final Answer:
The total number of words that begin with 'R' and end with 'W' in the word "RAINBOW" is **120**.

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