Answer these questions independently of each other
In the different arrangements of the word RAINBOW how many words begin with R?

Options

A. 720
B. 360
C. 1440
D. 480

Answer

To solve the problem of how many different arrangements of the word "RAINBOW" begin with the letter R, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Letters**: The word "RAINBOW" consists of 7 letters: R, A, I, N, B, O, W.

2. **Fix the First Letter**: Since we want the arrangements to begin with the letter R, we fix R in the first position.

3. **Count Remaining Letters**: After fixing R, we are left with the letters A, I, N, B, O, W. This gives us a total of 6 letters to arrange.

4. **Calculate Arrangements**: The number of ways to arrange these 6 letters can be calculated using factorial notation. The number of arrangements of n distinct objects is given by n!. Therefore, we need to calculate 6!.

5. **Calculate 6!**:
- 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720.

6. **Conclusion**: Thus, the total number of different arrangements of the word "RAINBOW" that begin with the letter R is 720.

### Final Answer:
The number of words that begin with R is **720**.

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