Question

To win at LOTTO in one​ state, one must correctly select 4 numbers from a collection of

45 numbers​ (1 through 45​). The order in which the selection is made does not matter. How many different selections are​ possible?

Answer 1

There are 1,480,700 different selections possible when choosing 4 numbers out of 45 for the LOTTO game as calculated using the combination formula C(n, k) where n is the total number of available numbers and k is the number of numbers to select.

Step-by-step explanation:

To win at LOTTO in a given state where one must correctly select 4 numbers from a collection of 45 numbers without considering the order, the number of different selections possible can be determined using combinations, also known as a binomial coefficient.

We use the combination formula which is defined as 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 '!' represents factorial which means the product of all positive integers up to that number.

For our LOTTO game, n = 45 and k = 4.

Using the formula:

• C(45, 4) = 45! / (4!(45-4)!)
• C(45, 4) = 45! / (4! * 41!)
• C(45, 4) = (45 * 44 * 43 * 42) / (4 * 3 * 2 * 1)
• C(45, 4) = 1,480,700

Therefore, there are 1,480,700 different selections possible when choosing 4 numbers out of 45 without regard to the order.