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GMAT Combinatorics: Permutations vs. Combinations (and Shorthand!)

GMAT Combinatorics Questions: Permutations vs. Combinations (plus Shorthand!) As noted above, this is simply a clipped factorial.  Let’s take the case from above and modify it slightly.  Three paintings, from a group of seven total paintings, are chosen to be hung on a wall. In how many ways can these three paintings be arranged? So: … Read More

GMAT Probability Question SOLVED: An Exception to the “At Least” Rule?

A GMAT Probability Question Fully Solved: An Exception to the “At Least” Rule? It’s difficult to say that there’s really an exception–after all, you can do any Probability question multiple ways, forward, backward, or even sideways. The question is just which of these ways will be most effective in the given situation. What is the … Read More

GMAT Combinatorics : Ultimate Guide to GMAT Permutations and Combinations

GMAT Combinatorics: an Introduction At the risk of blowing all the secrets too early, let’s do this at the beginning. If you can answer three Core Questions, you’ll be able to answer any Combinatorics question that the GMAT decides to throw at you. Here they are: How Many Spaces? How Many Choices? Does Order Matter? … Read More

Collapsing Probabilities in GMAT Probability: Part Deux

Collapsing Probabilities: Part Deux — for Part Un, Click Here This one I’m only doing with the “Collapsing Probabilities” technique. You’re welcome to do it by making your choice first, then multiplying by the number of potential choices. It’s just that I won’t. You can e-mail me if you need your hand held. Here’s the … Read More

Collapsing Probabilities in GMAT Probability

Collapsing Probabilities in GMAT Probability Unsurprisingly, there’s more than one way to look at this phenomenon. Let’s take a look at this straightforward case… Bag 1 contains forty marbles numbered consecutively from 11 to 50. Bag 2 contains fifty marbles numbered consecutively from 41 to 90. If one marble is selected from each bag, what … Read More

GMAT Probability: Number of Distributions x Probability per Distribution

GMAT Probability and Number of Distributions x Probability per Distribution The Independent Probability Case for GMAT Probability Now, let’s go back to the example from the previous page, which we can rephrase as this:If a coin is flipped five times, what is the Probability that it will land on Heads only once?That gives us a … Read More

“At Least” Problems in GMAT Probability

“At Least” Problems in GMAT Probability Hey, remember how all the Probabilities have to be fractions less than one? I mean, after all, it’s reasonably rare for there to be a greater than 100% chance that something will happen. The other thing to bear in mind is that a full Probability–anything that is forgone conclusion–is … Read More