(b) There are 16 appetizers available at a restaurant. From these, Charmaine is to choose 13 for her party. How many groups of 13 appetizers are possible?

Step 1 ：This is a combination problem. We are choosing 13 appetizers out of 16, and the order in which we choose them does not matter.

Step 2 ：The formula for combinations is: \(C(n, k) = \frac{n!}{k!(n-k)!}\)

Step 3 ：In this case, \(n = 16\) (the total number of appetizers) and \(k = 13\) (the number of appetizers Charmaine is choosing).

Step 4 ：Let's plug these values into the formula: \(C(16, 13) = \frac{16!}{13!(16-13)!}\)

Step 5 ：First, calculate the factorials: \(16! = 16 \times 15 \times 14 \times 13 \times 12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1\), \(13! = 13 \times 12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1\), and \((16-13)! = 3! = 3 \times 2 \times 1\)

Step 6 ：Now, substitute these values back into the formula: \(C(16, 13) = \frac{16!}{13!(16-13)!} = \frac{16 \times 15 \times 14 \times 13!}{13! \times 3!} = \frac{16 \times 15 \times 14}{3 \times 2 \times 1} = 560\)

Step 7 ：So, there are \(\boxed{560}\) different groups of 13 appetizers that Charmaine can choose from the 16 available.