Step 1 :This problem is about combinations. The person can choose 2 bags out of 16, and the order in which she chooses them does not matter. Therefore, we can use the combination formula, which is nCr = n! / [(n-r)! * r!], where n is the total number of items, r is the number of items to choose, and '!' denotes factorial.
Step 2 :Let's denote the total number of varieties as n, and the number of bags the person needs to choose as r. In this case, n = 16 and r = 2.
Step 3 :Substitute n and r into the combination formula: \(C = \frac{n!}{(n-r)!r!} = \frac{16!}{(16-2)!2!}\)
Step 4 :Simplify the above expression to get the final answer.
Step 5 :Final Answer: The person can make \(\boxed{120}\) different selections.