Final answer:
The probability that 8 different-sized washers arranged in a row will be in order of size is 1 over the factorial of 8 (1/40,320).
Step-by-step explanation:
The question is asking to find the probability that if 8 different-sized washers are arranged in a row, they will be arranged in order of size. There is only one way to arrange the washers in ascending or descending order by size. However, there are a total of 8! (factorial of 8) possible arrangements when the order of these washers is considered since each has a unique size.
Therefore, the probability is calculated as the ratio of the favorable arrangement to the total possible arrangements:
- Find the total number of arrangements: 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320
- Since there is only one favorable outcome, the probability = 1/40,320