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?
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.