Final answer:
The probability of winning the lottery by matching three numbers chosen from 1 to 9 in exact order is 1 out of 504. None of the provided answer choices is correct, but 1/252 is the closest approximation if a choice must be made from the options given.
Step-by-step explanation:
To calculate the probability of winning a lottery where three numbers are randomly chosen from 1 to 9, we need to consider that the numbers are chosen without replacement, meaning the same number cannot be selected more than once. Since there are 9 possible numbers for the first number, 8 remaining for the second, and 7 remaining for the third, the total number of different sequences of 3 numbers we can have is 9 × 8 × 7 = 504. Since the order in which the numbers are drawn matters, this is a permutation, not a combination.
Assuming you must match the numbers in the exact order, to win you need to have one specific sequence of 3 numbers. There is only 1 winning sequence out of 504 possible sequences. Thus, the probability you have the winning sequence is 1/504.
None of the answer choices exactly match this result, but if the question had an error or typo and was supposed to indicate a probability out of those provided, choice d) 1/252 would be closest to the actual probability and could potentially be selected as an approximation if you are required to choose from the options given.