Final answer:
The probability of winning the lottery with a single ticket, where seven balls are drawn from 18 and the order does not matter, is 1 divided by the number of combinations, which is 1/31,824.
Step-by-step explanation:
The question asks us to compute the probability of winning a lottery where 7 balls are drawn from a total of 18. Since order does not matter, we can calculate the probability using combinations. The total number of ways to draw 7 balls out of 18 is expressed as the combination 18 choose 7, which is calculated as 18! / (7!(18-7)!).
Only one combination matches the lottery ticket, so the probability of winning is 1 divided by the total number of combinations. Using a calculator, we find that there are 31,824 possible combinations, so the probability of a single ticket winning is 1/31,824.