Find the number of ways to arrange the letters in REVOLVER.

Question

UpStudy AI · Accepted Answer

To determine the number of distinct ways to arrange the letters in the word **REVOLVER**, we'll follow these steps:

1. **Identify the letters and their frequencies:**
   - R: 2
   - E: 2
   - V: 2
   - O: 1
   - L: 1

So, there are a total of **8 letters** with some repeated letters.

2. **Use the formula for permutations of multiset:**

The number of distinct arrangements is given by:

$$
   \frac{n!}{n_1! \times n_2! \times \dots \times n_k!}
   $$

Where:
   - $$ n $$ is the total number of letters.
   - $$ n_1, n_2, \dots, n_k $$ are the frequencies of the repeated letters.

3. **Plug in the values:**

$$
   \frac{8!}{2! \times 2! \times 2!} = \frac{40320}{8} = 5040
   $$

Here's the breakdown:
   - $$ 8! = 40320 $$
   - $$ 2! \times 2! \times 2! = 8 $$
   - $$ \frac{40320}{8} = 5040 $$

**Therefore, there are 5,040 distinct ways to arrange the letters in "REVOLVER."**

**Answer:** 5040
There are 5,040 distinct ways to arrange the letters in "REVOLVER."

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