<p><a href="https://www.prepswift.com/quizzes/quiz/prepswift-combinations" target="_blank">Combinations Exercise</a></p>
<p><strong>NOTE</strong>: about 3:18 into the video, Greg says something on the lines of "you'll shake hands with 435 people". Clearly he meant to say that "there will be 435 handshakes in total"</p><p>As discussed in the previous mountain entry titled Intoduction to Combinatorics, <strong><span style="color:#8e44ad;">Combinations </span></strong>refer to the number of possible groupings of a certain set of items where order is NOT important. For example, if a basketball team consists of Sarah, Beth, and Tiffany, that is no different than it consisting of Beth, Tiffany, and Sarah. That's the same thing. Those are not two different cases. This is what we mean by combinations.</p>
<p><strong><span style="color:#27ae60;">The Formula</span></strong></p>
<p>$$\frac{n!}{r!(n-r)!}$$</p>
<p><i>where $n$ is to the total number of elements and $r$ is the size of each grouping</i></p>
<p><strong><span style="color:#e74c3c;">Example</span></strong></p>
<p>Billy Bob has $10$ different novels. He's going to take $4$ of them on his travels. How many different $4$-novel combinations are possible?</p>
<p>$$n= 10, r =4$$</p>
<p>$$\frac{10!}{4!(10-4)!} = \frac{10!}{4!6!} = 210$$</p>