Combinations

<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 &quot;you&#39;ll shake hands with 435 people&quot;. Clearly he meant to say that &quot;there will be 435 handshakes in total&quot;</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&#39;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&#39;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>