o win at LOTTO in one​ state, one must correctly select 5 numbers from a collection of 48 numbers​ (1 through 48​). The order in which the selection is made does not matter. How many different selections are​ possible?

Answer 1

To calculate the number of different selections possible in this LOTTO game, we can use the combination formula:

C(n, k) = n! / (k! * (n - k)!)

Where:
n = total number of items
k = number of items to choose at a time
! = factorial

In this case, n = 48 and k = 5. Plugging these values into the formula, we get:

C(48, 5) = 48! / (5! * (48 - 5)!)
C(48, 5) = 48! / (5! * 43!)
C(48, 5) = (48 * 47 * 46 * 45 * 44) / (5 * 4 * 3 * 2 * 1)
C(48, 5) = 1,712,304

Therefore, there are 1,712,304 different selections possible in the LOTTO game.