To determine the number of selections that can be made using the original shipment of 20 graphing calculators, we can use the concept of combinations.
The formula for calculating combinations is represented as "nCr," where n is the total number of items and r is the number of items to be selected from the total.
In this case, we have 20 graphing calculators, and we want to select 4 of them. So, we can calculate the number of selections using 20C4.
The formula for nCr is:
nCr = n! / [(n-r)! * r!]
First, let's calculate n! (factorial of n):
20! = 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
Next, let's calculate (n-r)!
(20-4)! = 16! = 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
Lastly, let's calculate r!
4! = 4 x 3 x 2 x 1
Now, substitute the values into the formula for nCr:
20C4 = 20! / [(20-4)! * 4!]
= (20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / [(16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) * (4 x 3 x 2 x 1)]
Calculating this expression will give us the total number of selections that can be made using the original shipment of graphing calculators.