How do we know this is a COMBINATION situation instead of a permutation question? The math here is a little more complicated without a combinatorics formula, but we’re just going to focus on the conceptual element for the moment. I want to know how many possible groups of three dishes out of the original 50 could potentially be selected by the judges to move on to the state competition. A first, a second, and a third prize will be given to the top three dishes, which will then have the honor of competing at the state competition in a few months. Suppose there’s a local food competition, and I’m told that a group of judges will taste 50 dishes at the competition. But what does such a situation look like? So, what about COMBINATIONS ? Obviously if we care about order for permutations, that implies we do NOT care about order for combinations. (It’s helpful to memorize factorials up to 6!) Combinations Example The quantity 5*4*3*2*1 is also often represented by the exclamation point notation 5!, or 5 factorial. The final step is to simply multiply these numbers to get 5*4*3*2*1 = 120 arrangements of the five paintings. We have five options at the start for the first slot:Īfter that painting is in place, there are four remaining that are available for the next slot:įrom there, the pattern continues until all slots are filled: Mathematically, how would we answer this question? Well, quite simply, we would consider the number of options we have for each “slot” on the wall. This is what defines this situation as a PERMUTATION problem. Let’s call the paintings A, B, C, D, and E:Įach of the above three is considered distinct in this problem, because the order, and thus the arrangement, changes. It’s the word “arrange” that often gives away that we care about the order in which the paintings appear. Suppose we have five paintings to hang on a wall, and we want to know in how many different ways we can arrange the paintings.
Let’s look at these concrete examples to make things a little clearer: Permutations Example
Quite simply, it’s whether we care about the order of the elements involved. It’s important to understand conceptually what makes permutations and combinations differ from one another. To start, let’s look at one of the most commonly asked questions related to GMAT combinatorics, namely the difference between combinatorics and permutations : Does Order Matter? But the good news is that, despite the scary title, what you need to know for GMAT combinatorics problems is actually not terribly complex. And it makes sense because so few of us are taught anything about it growing up. It’s a phrase that’s stricken fear in the hearts of many of my students.
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