1. **State the problem:** We want to find the probability that a rearrangement of the letters in the word "SUNDAY" begins with the letter Y and ends with the letter S. 2. **Total number of arrangements:** The word "SUNDAY" has 6 distinct letters. The total number of ways to arrange these letters is $$6! = 720$$. 3. **Number of favorable arrangements:** We want arrangements starting with Y and ending with S. - Fix Y at the first position and S at the last position. - The remaining 4 letters (U, N, D, A) can be arranged in the middle positions. - Number of ways to arrange these 4 letters is $$4! = 24$$. 4. **Calculate the probability:** $$\text{Probability} = \frac{\text{Number of favorable arrangements}}{\text{Total number of arrangements}} = \frac{4!}{6!} = \frac{24}{720}$$ 5. **Simplify the fraction:** $$\frac{24}{720} = \frac{\cancel{24}}{\cancel{720}} = \frac{1}{30}$$ 6. **Final answer:** The probability that the word begins with Y and ends with S is $$\boxed{\frac{1}{30}}$$.