What is the probability that if 4 letters are typed, no letters are repeated? Write your answer in decimal form, rounded to the nearest thousandth. The probability that no letters are repeated is Question Help: Video Message instructor
Solution
Step 1 ：The first letter can be any of the 26 letters, so the probability is \(\frac{26}{26} = 1\).
Step 2 ：The second letter must be different from the first, so there are only 25 choices left. The probability is \(\frac{25}{26}\).
Step 3 ：The third letter must be different from the first two, so there are only 24 choices left. The probability is \(\frac{24}{26}\).
Step 4 ：The fourth letter must be different from the first three, so there are only 23 choices left. The probability is \(\frac{23}{26}\).
Step 5 ：To find the overall probability, we multiply the probabilities from each step: \(1 \times \frac{25}{26} \times \frac{24}{26} \times \frac{23}{26} = 0.6588\).
Step 6 ：So, the probability that no letters are repeated when 4 letters are typed is approximately \(\boxed{0.659}\) when rounded to the nearest thousandth.
