Question

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)

Answer 1

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.