As we learned in this module, counting goes well beyond learning how to count numbers in the first years of elementary school. In fact, combinatorics is a field of mathematics dedicated solely to the science of counting.

Determining the number of arrangements or ways to select a small number of items is a relatively simple task. With a large number of items, however, the process can become very complicated. For example, think about all the possible combinations of numbers in lottery tickets or all the different seating arrangements at a big event.

For this discussion, complete the following tasks:

Share a detailed example in which you need to use the Basic Counting Rule, permutations, or combinations to find the different ways to arrange or select different objects or people.
Include your calculations to solve this counting problem, and discuss your steps in detail.