Eight names are put on a ballot in a randomly selected order. What is the probability that they are not in alphabetical order?
The probability that the names are not in alphabetical order is $\square$.
(Type an integer or a simplified fraction.)
Answer
Final Answer: The probability that the names are not in alphabetical order is \(\boxed{0.9999751984126984}\).
Step 1 ：Calculate the total number of ways to arrange 8 names, which is \(8!\).
Step 2 ：Calculate the probability that they are in alphabetical order, which is \(1/8!\).
Step 3 ：Subtract this probability from 1 to find the probability that they are not in alphabetical order.
Step 4 ：The total number of ways to arrange 8 names is \(40320\).
Step 5 ：The probability that they are in alphabetical order is \(2.48015873015873 \times 10^{-5}\).
Step 6 ：The probability that the names are not in alphabetical order is \(1 - 2.48015873015873 \times 10^{-5}\).
Step 7 ：Final Answer: The probability that the names are not in alphabetical order is \(\boxed{0.9999751984126984}\).
