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Permutations and combinations are connected counting methods. Combinations count selections where order does not matter, while permutations count arrangements where order matters. nPr = nCr × r!. Example: choosing 3 of 5 gives 5C3 = 10, arranging them gives 5C3 x 3! = 5P3 = 60.
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Permutations and combinations are two connected ideas in counting. A combination focuses on selection when order does not matter, while a permutation extends the idea by considering the different arrangements of the selected elements. Understanding this link is an important step in GMAT preparation, since it shows how one concept grows out of the other and why the formulas are related. For example, selecting a group reflects combinations, and assigning order to that group reflects permutations. With this perspective, the topic becomes easier to interpret, and the logic behind problems more intuitive.
Permutations and combinations may look like two separate ideas, but in reality, they are closely related. Combinations form the foundation, and permutations build upon them.
A combination answers the question: How many ways can I select a group from a larger pool when the order of selection does not matter?
For example, if 11 speakers are to be chosen from a group of 20, we use 20C11.
Here, it does not matter whether a particular speaker is chosen first or last; what matters is simply who is on the team.
A permutation answers a slightly different question: How many ways can I select and then arrange a group when order matters?
Taking the same example, if the 11 selected speakers also need to be assigned speaking order, then order becomes important. In that case, we use 20P11.
The connection lies in the fact that permutations are nothing more than combinations multiplied by the number of ways the selected elements can be arranged. Mathematically, this means:
nPr = nCr × r!
Therefore,
20P11 = 20C11 × 11!.
Both approaches yield the same result, whether you directly calculate the permutation or break it into two steps.
Combinations count selections, while permutations extend this by including the different possible orders. Recognizing this relationship helps you approach counting problems with clarity. Consistent practice and an adequate number of GMAT mocks will ensure that the distinction becomes second nature under timed conditions.
Permutations and combinations highlight the balance between order and choice. In GMAT preparation, progress depends on knowing when the sequence of tasks matters and when the outcome alone is important. Practice schedules, essay deadlines, and time management require order, while school selection and values call for thoughtful choice. In the MBA application process, this clarity helps you act with precision while avoiding wasted effort. Life too offers the same lesson: sometimes order determines success, and sometimes essence is enough. Learning to distinguish the two builds discipline, wisdom, and confidence that extend well beyond academics.
