To win at LOTTO in a certain state, one must correctly select 6 numbers from a collection of 55 numbers (one through 55.) The order in which the selections is made does not matter. How many different selections are possible?

Step 1 ：This problem is about calculating the number of combinations. In combinatorics, a combination is a selection of items without considering the order. In this case, we are selecting 6 numbers out of 55, and the order does not matter.

Step 2 ：The formula for combinations is: \(C(n, k) = \frac{n!}{k!(n-k)!}\), where n is the total number of items, k is the number of items to choose, and '!' denotes factorial, which is the product of all positive integers up to that number.

Step 3 ：In this case, n = 55 (the numbers from 1 to 55) and k = 6 (we need to choose 6 numbers). So we need to calculate C(55, 6).

Step 4 ：By substituting the values into the formula, we get: \(C(55, 6) = \frac{55!}{6!(55-6)!}\)

Step 5 ：After calculating the above expression, we find that the number of different selections possible is 28989675.

Step 6 ：Final Answer: The number of different selections possible is \(\boxed{28989675}\)