Final answer:
To calculate the number of different sets of 6 numbers that can be chosen from 1 to 57, the combination formula C(57, 6) is used, resulting in the calculation of 57! divided by the product of 6! and 51!, which represents the distinct combinations possible.
Step-by-step explanation:
To find out how many different sets of 6 numbers can be chosen from 1 to 57, we use the combination formula which is C(n, k) = n! / (k!(n - k)!), where n is the total number of items to choose from, and k is the number of items to choose. In the case of the lottery question, there are 57 possible numbers, and players must choose 6, so n = 57 and k = 6.
Thus, the number of different sets of 6 numbers is calculated as follows:
C(57, 6) = 57! / (6! * (57 - 6)!) = 57! / (6! * 51!) = (57 * 56 * 55 * 54 * 53 * 52) / (6 * 5 * 4 * 3 * 2 * 1)
After simplifying, we get the number of different combinations possible for choosing 6 numbers out of 57.