Problem

A person going to a party was asked to bring 2 different bags of chips. Going to the store, she finds 16 varieties.
How many different selections can she make?

Answer

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Answer

Final Answer: The person can make \(\boxed{120}\) different selections.

Steps

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.

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