Give an example problem where you would use Combination skills and formula to solve. Solve your example problem showing all your steps. (Hint: you could use an example from class or a previous quick check - DO NOT use one you find via google.)(3 points)
Example problem:
A group of 5 friends is going out to eat. They want to choose 2 appetizers from a menu of 8 options. How many different ways can they choose the appetizers?
Solution:
To solve this problem, we will use the combination formula, which is given by:
C(n, k) = n! / (k!(n-k)!),
where n is the total number of items to choose from, k is the number of items to choose, and ! denotes factorial (the product of all positive integers up to that number).
In this case, n = 8 (total number of appetizer options) and k = 2 (number of appetizers to choose).
Plugging these values into the combination formula, we get:
C(8, 2) = 8! / (2!(8-2)!)
C(8, 2) = 8! / (2!6!)
C(8, 2) = (8 x 7 x 6!) / (2! x 6!)
C(8, 2) = (8 x 7) / 2!
C(8, 2) = 56 / 2
C(8, 2) = 28
Therefore, there are 28 different ways the group of 5 friends can choose 2 appetizers from the menu of 8 options.