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Permutations and combinations are core counting tools in GMAT Quant. Permutations apply when order matters: nPr = n! / (n − r)!. Combinations apply when order does not matter: nCr = n! / [r!(n − r)!]. Example: from 6 items, arranging 4 gives 6P4 = 360; choosing 4 gives 6C4 = 15.
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Many students find themselves confused about when to apply permutations and when to apply combinations. The formulas may look similar, but the thinking behind them is very different. The key lies in understanding whether order matters or not. If order matters, we are working with permutations; if order does not matter, it is a combination. To truly grasp this, it helps to look at practical examples, such as arranging children in a row or forming a team from a larger group. Each case follows a logical approach that determines whether we apply nPr or nCr. Mastering this distinction during your GMAT prep not only improves accuracy but also saves time during the test. In this video, you will learn the step-by-step logic of how permutations and combinations work.
Permutations and combinations are at the heart of many GMAT problems. The real challenge is knowing when to apply which concept, and that clarity comes from observing whether the sequence of arrangement plays a role.
If order is important, we use permutations. For example, if there are 10 children and 10 chairs, the total number of possible arrangements is 10! because every seat will be filled and every order creates a new outcome. This is written as 10P10. Similarly, if 6 children are to be selected out of 10 and seated in a row, the number of choices is 10P6, since the arrangement of those selected also matters.
When the question is about forming a group where order does not matter, we use combinations. For instance, if 6 children are to be chosen from 10 to form a team, the total ways are 10C6. Here, different orders of the same group are not counted separately.
If 4 children are to be chosen out of 6 and seated in a row, the order matters, so the result is 6P4 = 360. If only selection is needed, the order does not matter, and the result is 6C4 = 15.
Permutations usually yield larger values than combinations because every distinct order is treated as a separate case, while combinations eliminate repeated orders. To internalize this distinction and build speed, attempt full-length GMAT simulations and observe how such concepts appear in real test scenarios.
Permutations and combinations remind us that success depends on knowing when order matters and when it does not. In GMAT preparation, order matters when you plan study schedules and attempt questions under time, but it does not when you reflect on lessons learned across practice sessions. In the MBA application process, order shapes deadlines and sequencing of tasks, while the essence lies in the choices that define your story. In life too, clarity comes from this distinction: when to focus on sequence and when to focus on substance. Wisdom lies in balancing both with awareness and consistency.
