Multiplication: The "Choice" Method

<p><span style="font-size:22px"><a href="https://www.prepswift.com/quizzes/quiz/prepswift-multiplication-the-choice-method" target="_blank">Multiplication: The &quot;Choice&quot; Method Exercise</a></span></p> <p><strong>Notes</strong>:</p> <ul> <li>around 4 minutes into the video, assume that we can have only one flavour in the ice-cream.</li> <li>around 6 minutes into the video, it says that the number of ice cream concoctions&nbsp;is 10 &times;&nbsp;2<sup>6</sup>&nbsp;- 1 = 639. This is <strong>not </strong>quite right. The reason is that the video remarks that there is only one way of creating an ice-cream without&nbsp;choosing any toppings, while the question says that there are 10 different flavours of ice-cream. This means that we actually have 10 ways of choosing an ice-cream without a topping, and that the correct answer is&nbsp;10 &times;&nbsp;2<sup>6</sup>&nbsp;- 10 =&nbsp;<strong>630</strong>.&nbsp;</li> </ul><p><strong><span style="color:#8e44ad;">The &quot;Choice&quot; Method</span></strong> is a great way to solve problems that ask you to calculate the &quot;number of ways&quot; you can do something.&nbsp;</p> <p>How It Works</p> <p style="margin-left: 40px;"><strong><u>Step 1</u></strong>: Write out the number of hash marks that corresponds to the number of categories in the problem.</p> <p style="margin-left: 40px;"><strong><u>Step 2</u></strong>: For each category, and on top of each hash mark, write out the number of choices that you have.</p> <p style="margin-left: 40px;"><strong><u>Step 3</u></strong>: Multiply these numbers together. Boom.</p> <p><strong><span style="color:#e74c3c;">Example</span></strong></p> <p>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?</p> <p style="text-align: center;"><u>$4$</u> $\times$ <u>$7$</u>&nbsp;$\times$ <u>$3$</u> $=84$</p> <p style="text-align: center;"><span style="color:#2980b9;"><em>Imagine there are little horizontal hash marks below each number.</em></span></p> <p><strong><span style="color:#e74c3c;">Another Example</span></strong></p> <p>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?</p> <p>$$2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2= 1024$$</p> <p style="text-align: center;"><span style="color:#2980b9;"><em>Imagine there are little horizontal hash marks below each number.</em></span></p> <p>$$2^{10} = 1024$$</p> <p>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.</p>