1. **State the problem:** We want to find the number of unique ways to arrange the letters in the word PRETTY.
2. **Identify the letters and their frequencies:** The word PRETTY has 6 letters: P, R, E, T, T, Y. Note that the letter T appears twice.
3. **Formula for permutations with repeated elements:** When some elements repeat, the number of unique arrangements is given by:
$$\frac{n!}{n_1! \times n_2! \times \cdots}$$
where $n$ is the total number of letters, and $n_1, n_2, \ldots$ are the frequencies of each repeated letter.
4. **Apply the formula:** Here, $n=6$ (letters in PRETTY), and the letter T repeats twice, so $n_1=2$.
5. **Calculate factorials:**
$$6! = 720$$
$$2! = 2$$
6. **Calculate the number of unique arrangements:**
$$\frac{6!}{2!} = \frac{720}{2} = 360$$
**Final answer:** There are 360 unique ways to arrange the letters in the word PRETTY.
Arrangements Pretty C79Ee4
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