To win at LOTTO in one state, one must correctly select 7 numbers from a collection of 47 numbers (1 through 47). The order in which the selection is made does not matter. How many different selections are possible?
To find the number of different selections possible, we can use the combination formula.
The number of ways to choose 7 numbers out of a collection of 47 numbers is given by the combination formula:
C(n, k) = n! / (k!(n-k)!)
where n is the total number of numbers in the collection (47) and k is the number of numbers we want to choose (7).
Plugging in the values:
C(47, 7) = 47! / (7!(47-7)!)
C(47, 7) = 47! / (7! * 40!)
C(47, 7) = (47 x 46 x 45 x 44 x 43 x 42 x 41) / (7 x 6 x 5 x 4 x 3 x 2 x 1)
C(47, 7) = 101,499,720
Therefore, there are 101,499,720 different selections possible when choosing 7 numbers from a collection of 47 numbers.