Permutations

<a href="https://www.prepswift.com/quizzes/quiz/prepswift-permutations" target="_blank">Permutations Exercise</a>As discussed in the previous mountain entry, Permutations are the number of arrangements where order is important. Tip: If you see a problem mention anything about "position," "ranking," "order," "arranged," or "arrangements," you're likely dealing with permutations. The Formula $$\frac{n!}{(n-r)!}$$ where $n$ is the total number of elements and $r$ is the number of choices Example From Previous Mountain Entry  Five individuals enter a race that awards a different prize for 1st, 2nd, and 3rd place. In how many different ways can these awards be distributed? Note that this is a problem dealing with "rankings," which tells us it's time to use the permutation formula where $n=5$ and $r=3$. $$\frac{5!}{(5-3)!} = \frac{5!}{2!} = 5 \times 4 \times 3 = 60$$  Isn't This Just the Choice Method? Yeah, kind of. Notice if we solve the problem above using the "choice" method, we get the same answer: $$5 \times 4 \times 3 = 60$$