Final answer:
The probability of winning a lottery by selecting six out of 50 numbers is calculated using the combination formula. There are 15,890,400 different combinations possible, thus the probability with a single ticket is 1 in 15,890,400.
Step-by-step explanation:
To calculate the probability of winning the lottery by selecting six out of 50 numbers from 0 to 49, we use the combination formula which allows for the arrangement of numbers in any order. The formula for a combination is C(n, k) = n! / (k!(n - k)!), where n is the total number of options, k is the number of options to choose, and '!' represents factorial.
In this case, we are choosing 6 numbers (k) from a total of 50 (n), the calculation would be C(50, 6). After calculating, we see that the number of different possible combinations is 15,890,400. Therefore, the probability of winning the lottery with a single ticket is 1 in 15,890,400.