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Permutations and combinations are counting methods in GMAT Quant. Permutations apply when order matters, such as seating 5 students in a row, giving 5P5 = 120 ways. Combinations apply when order does not matter, such as choosing 4 speakers from 7, giving 7C4 possible selections.
Many GMAT aspirants face confusion about when to apply permutations and when to apply combinations. The difference may appear subtle, yet it changes the entire approach to a problem. The first key is to ask whether the sequence matters. If order matters, then we are working with permutations. If order does not matter, it becomes a case of combinations. This distinction determines whether the answer will involve multiplying arrangements or eliminating repeated orders. For example, seating children in a row is about arrangements, while forming a team is about selection. With this clarity, even large questions with many elements can be solved systematically. In this video, you will see examples that bring this concept to life in a simple and practical way. To refine your preparation, strengthen your fundamentals through a comprehensive GMAT preparation course and build exam-level confidence with adequate GMAT practice tests.
A common challenge in counting problems is deciding whether to use permutations or combinations. The choice depends entirely on whether order matters in the given situation.
Consider the question: In how many ways can 5 boys be seated in a row?
Here, 5 elements are placed in 5 positions, and every arrangement creates a new possibility.
Order matters, so the answer is 5! = 120.
This is a straightforward application of permutations.
Now think about forming a team of 11 speakers out of 20.
A team is defined by who is chosen, not the sequence in which they are listed.
Therefore, order does not matter, and the answer is 20C11.
There are also cases where both selection and arrangement are part of the problem.
For example, consider a scenario when out of 20 speakers, 11 must be selected, and their speaking order needs to be decided.
This becomes 20P11.
Another way to look at it is first selecting 11 (20C11) and then arranging them in 11! ways.
Therefore, 20C11 x 11! ways.
Both methods lead to the same result.
Permutations and combinations are closely connected because both deal with selecting elements from a set. The key relation is:
nPr = nCr × r!
Permutations count every possible order, while combinations remove repeated orders.
For example, choosing 3 students out of 5 is 5C3 = 10. If these 3 students must also be seated in order, the result is 5C3 x 3! which is same as 5P3.
Thus, permutations are simply combinations multiplied by the number of ways to arrange the chosen elements.
Permutations are used for arrangements where order plays a role. Combinations are for selections where order does not matter. Being able to make this distinction quickly is essential for accuracy and speed in GMAT counting problems. Regularly attempting full GMAT simulation will help you strengthen this clarity under exam-like conditions.
Permutations and combinations remind us that clarity comes from asking the right question. In GMAT preparation, you often face choices where sequence shapes meaning, and others where only the selection matters. Recognizing this distinction builds accuracy and speed. The MBA applications process mirrors the same truth: some steps require precise order, such as scheduling exams, essays, and recommendations, while others are about the choices themselves, like which schools align with your goals. Life too alternates between these perspectives. Wisdom lies in knowing when order defines the outcome and when essence alone carries the weight of decision.
