Question

To win the lottery in a certain state, you must correctly select six numbers from a pool of numbers 1 to 52. You win if your numbers match the winning numbers in any order.

How many different selections are possible?

Answer 1

To calculate the number of different lottery selections possible, one must use the combinations formula. For selecting six numbers from a pool of 52, the formula yields 20,358,520 different selections.

Step-by-step explanation:

To determine the number of different selections possible when picking six numbers from a pool of 1 to 52 for a lottery, we use combinations because the order of the numbers does not matter. The formula for a combination is given by C(n,k) = n! / (k!(n-k)!), where n is the total number of items, and k is the number of items to choose. In this case, n=52 and k=6.

The calculation is as follows:

C(52,6) = 52! / (6!(52-6)!) = 52! / (6! * 46!) = 20,358,520

Therefore, there are 20,358,520 different selections possible.