![]() ![]() ![]() We have then chosen one painting, meaning that we have six choices for the second space, etc. In other words, we have seven choices for the first space. What this means in practice, of course, is that we can simply fill the spaces, counting down from seven. We have seven things, so that of course means that we can choose from–wait for it– seven paintings! This one’s probably easier on the surface. I guess we could theoretically say eight, nine, or 37 spaces, but there are only seven total things to count so we’re still limited back to seven. This is sort of convenient, isn’t it? We don’t have any restriction on the spaces, so in this case the number of spaces is simply the number of objects: that is, seven total spaces because there are seven paintings. Let’s start with the Core Questions as discussed in the Introduction: How Many Spaces? That is, we have no restriction on which particular paintings we’re hanging–rather, we can just put them any damn place we please. In how many ways can the seven paintings be arranged? There are seven paintings to hang on a wall, and there are an unlimited number of places that we can hang them. The idea of a Factorial is best described in situ: ![]() If we don’t get the concept of Factorials straight, the rest of this is never going to work. The first and only place to start our discussion of Permutations and Combinations problems is with Factorials. If, on the other hand, you are interested in learning GMAT Combinatorics the correct way, then step inside… Chapter 1: Factorials Now is the appropriate time to close this page and report me to the gods of unnecessary work. So–if your butt is sore by this point and you really want to learn about using those equations in an attempt to spend as long as humanly possible doing GMAT Permutations and Combinations / Combinatorics questions, then it’s your party (and you can cry if you want to). If you know how to build them, it’s pointless to memorize them, eh?Īllow me to further my point: we do not need these equations because 1) we are not using Excel and 2) we are not twelve. It is not worth your time to memorize these, or apply them (for that matter).Īs detailed in the book, we ultimately will make sure you are comfortable enough with the concepts to build these equations. If you can answer three Core Questions, you’ll be able to answer any Combinatorics question that the GMAT decides to throw at you.įiguring out the number of Spaces, Choices, and whether Order Matters are basically the substance of the rest of this post.Īs a note, I have a potentially violent disdain for the standard Permutation and Combinations equations: Permutation: n!/(n-r)! Combination: n!/(r!(n-r)!) At the risk of blowing all the secrets too early, let’s do this at the beginning. ![]()
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