To win at LOTTO in one state, one must correctly select 7 numbers from a collection of 52 numbers ( 1 through 52 ). The order in which the selection is made does not matter. How many different selections are possible?
There are different LOTTO selections.
Answer
Final Answer: \(\boxed{133,784,560}\)
Step 1 ：We are given a LOTTO game where one must correctly select 7 numbers from a collection of 52 numbers (1 through 52). The order in which the selection is made does not matter. We are asked to find out how many different selections are possible.
Step 2 ：This is a combination problem. In combinatorics, a combination is a selection of items without considering the order. The formula for combination is given by: \[C(n, k) = \frac{n!}{k!(n-k)!}\] 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 is 52 (the total number of LOTTO numbers) and k is 7 (the number of numbers to select).
Step 4 ：Substituting the given values into the combination formula, we get: \[C(52, 7) = \frac{52!}{7!(52-7)!}\]
Step 5 ：Solving the above expression, we find that there are 133,784,560 different LOTTO selections possible.
Step 6 ：Final Answer: \(\boxed{133,784,560}\)
