Final answer:
The probability that 9 different-sized washers are arranged in a row in order of size is 1 divided by 9!, or 1 in 362,880.
Step-by-step explanation:
To find the probability that 9 different-sized washers are arranged in a row in order of size, we recognize that there is only one way for them to be in the correct order. Since they are of different sizes, the question can be treated like a permutation problem where the arrangement matters. Given 9 washers, there are 9! (9 factorial) possible arrangements. The factorial of a number is the product of all positive integers less than or equal to that number, so 9! = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1.
Thus, the probability of them being in size order is 1 divided by the total number of arrangements:
Probability = 1 / 9! = 1 / 362880