The "Choice" Method is a great way to solve problems that ask you to calculate the "number of ways" you can do something.

How It Works

Step 1: Write out the number of hash marks that corresponds to the number of categories in the problem.

Step 2: For each category, and on top of each hash mark, write out the number of choices that you have.

Step 3: Multiply these numbers together. Boom.

Example

At a certain restaurant, you have the choice of four entrees, seven side dishes, and three desserts. If you must choose only one of each, how many different meals can you order?

$4$ $\times$ $7$ $\times$ $3$ $=84$

Imagine there are little horizontal hash marks below each number.

Another Example

A soon-to-be bride and grooom are looking at ten names on a list and deciding whether to extend an invitation to their wedding to each person. In how many different ways can the bride and groom send out (or not send out) invitations to these ten people?

$$2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2= 1024$$

Imagine there are little horizontal hash marks below each number.

$$2^{10} = 1024$$

In the above case, each potential guest is in their own category, and for each we have two choices: yes or no. So we multiply $2$ by itself ten times to get the correct answer.