Answer: 1287
Explanation:
The situation involves combinations.
Combinations are used when we want to count the number of ways to choose a subset of objects from a larger set, without regard to the order in which the objects are chosen. In this case, we want to count the number of ways to choose a five-member committee from a group of 13 people.
We don't care about the order in which the committee members are chosen, as long as we end up with a committee of five people. That is, the committee of Alice, Bob, Charlie, Dave, and Eve is considered the same as the committee of Eve, Charlie, Bob, Dave, and Alice.
Therefore, we can use the combination formula:
nCk = n! / (k! * (n-k)!)
where n is the number of objects to choose from, k is the number of objects to choose, and "!" represents the factorial function.
In this case, we want to choose 5 people from a group of 13:
13C5 = 13! / (5! * (13-5)!) = 13! / (5! * 8!) = (13 * 12 * 11 * 10 * 9) / (5 * 4 * 3 * 2 * 1) = 1,287
Therefore, there are 1,287 ways to choose a five-member committee from a group of 13 people, and we can use the combination formula to calculate this count.