Final answer:
To determine the number of different ways to select 6 numbers from 39, the combination formula C(39, 6) is used, which accounts for the selections where order does not matter.
Step-by-step explanation:
The question asks for the number of different ways to select 6 numbers out of 39 in a lottery. To solve this, we use the concept of combinations in probability since the order of selection does not matter. The formula for combinations is C(n, k) = n! / [k!(n - k)!], where n is the total number of items to choose from, k is the number of items to choose, and '!' denotes factorial.
For this scenario, n=39 and k=6, so C(39, 6) is the total number of different ways to select 6 numbers. Plugging in the values, we get 39! / [6!(39 - 6)!], which simplifies to 39! / (6! * 33!), resulting in the number of different possible selections. This is often calculated using a calculator or combinatorics software as it involves large factorial numbers.