Combinatorics: The SeBox (Selection Box)

2) Ask yourself - "how many Jackets can I choose from?" In this simple case, we have 5 jackets, so the box contains 5 possible jackets to select from. The SeBox will look like this:

$$\mathop{\fbox{5}} \limits^{\hbox{Jackets}}$$

5 is indeed the answer to the question.

We'll discuss the use of multiple SeBoxes later on. For now, just remember this:

[[summary]]

We begin our journey into Combinations land by introducing the concept of the Selection Box, or SeBox. A SeBox, as its name implies, is a box of selections. Every time a Combinations & Permutations question asks you to select one item out of many possible items (e.g. one jacket out of 5 possible jackets), you will model this Selection in a SeBox. This is the basis of our step-by-step method to solve C & P problems.

Let's look at this (very) simple example:

John has 5 jackets. How many ways are there for John to choose one jacket from his collection?

1) Draw a box with a label of "jackets" on top:

 $$\mathop{\fbox{}} \limits^{\hbox{Jackets}}$$

If John needed to also choose a pair of pants out of, for example, 4 possible pairs, that selection would merit its own SeBox, with a different label of "Pants".

Remember: Every item deserves its own SeBox.