(a) There are 17 appetizers available at a restaurant. From these, Charmaine is to choose 13 for her party. How many groups of 13 appetizers are possible?

The problem can be solved using the concept of combinations in mathematics. A combination is a selection of items where order does not matter. In this case, we are selecting 13 appetizers out of 17, and the order in which we select them does not matter.

The formula for combinations is:

C(n, r) = n! / [r!(n - r)!]

where:

• n is the total number of items,
• r is the number of items to choose,
• "!" denotes factorial, which is the product of all positive integers up to that number.

Substituting the given values into the formula:

C(17, 13) = 17! / [13!(17 - 13)!]

This simplifies to:

C(17, 13) = 17! / [13! * 4!]

Calculating the factorials and simplifying gives the number of ways Charmaine can choose 13 appetizers from 17.