Mastering Permutations and Combinations for the GRE

If you’re feeling a little tangled up in permutations and combinations, you’re not alone. These concepts are key players in many fields, including probability theory, statistics, and computer science. And yes, they also love to pop up in the GRE’s quantitative reasoning section. But don’t worry, we’ve got your back. Let’s untangle these topics together so you can tackle the GRE with confidence.

Permutation vs. Combination: What’s the Difference?

Before delving into strategies, let’s clarify the difference between permutations and combinations. Permutations deal with the arrangement of objects, considering the order of the elements, while combinations focus on selecting a subset of objects without regard to their order.

Picture this – you’ve got three books (A, B, C) and you want to choose all or some of them for your bookshelf. Every different choice also counts as a possible arrangement. That’s what permutations are all about: selection and arrangement. The formula? nPr = n! / (n – r)!, where ‘n’ is the total number of objects and ‘r’ is the number of objects arranged.

Let’s say you want to choose two of those books for your bookshelf. The formula would then be 3! / (3 – 2)!, which would then be 6 / 1 = 6. In other words, your options would be: 1. AB, 2. AC, 3. BA, 4. BC, 5. CA, 6. CB.

Now, imagine you’ve got those same three books, but this time, you will choose any two to read tonight. This time, while the choice matters, the order does not – that’s a combination. The formula? nCr = n! / (r! * (n – r)!), where ‘n’ is the total number of objects and ‘r’ is the number of selected objects.

3! / (2! * (3 – 2)!) = 6 / (2! * 1!) = 6 / 2 = 3

There are three possible combinations of books! These would be: 1. AB, 2. AC, 3. BC.

Strategies to Master Permutations and Combinations

Now that we’ve got the basics down, let’s move on to some killer strategies:

Understand the Concepts

Start by getting cozy with the definitions and formulas. Practice calculations using these formulas until they feel second nature.

Identify Problem Types

Get good at spotting the different types of permutation and combination problems that the GRE loves to throw at you. Practice categorizing problems to develop an intuitive approach for each type.

Work with Concrete Examples

Use real-world examples to reinforce your understanding. Visualize and manipulate objects to get a solid grasp of the concepts.

Practice, Practice, Practice

The more you practice, the better you’ll get. Start with simpler questions and gradually level up to more complex ones. Keep an eye out for patterns and shortcuts to save time during the exam.