Final answer:
To find the probability of picking one of the winning numbers from 1 to 20 when picking 4 numbers, use the combination formula to calculate the total number of possible outcomes and the number of favorable outcomes. Divide the number of favorable outcomes by the total number of possible outcomes to get the probability.
Step-by-step explanation:
To find the probability of picking one of the winning numbers, we need to first determine the total number of possible outcomes and then the number of favorable outcomes. In this case, we are picking 4 numbers from a set of 20 numbers.
The total number of possible outcomes is the number of ways to pick 4 numbers out of 20, which can be calculated using the combination formula: C(20, 4) = 20! / (4! * (20-4)!).
The number of favorable outcomes is the number of ways to pick 1 winning number out of 20, multiplied by the number of ways to pick 3 numbers from the remaining 19 numbers: 20 * C(19, 3).
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes: Probability = (20 * C(19, 3)) / C(20, 4).