Permutation and Combination Basics for Placements

Permutation and Combination Basics for Placements

Permutation and combination questions test your logical thinking and mathematical structure. These topics appear in placement aptitude tests of companies like Amazon, Microsoft, and Goldman Sachs. While the concepts seem complex at first, placement-level questions follow just a handful of standard patterns that can be mastered with focused practice.

Permutation vs Combination

Permutation counts arrangements where order matters. Combination counts selections where order does not matter. The key question is always: does order matter here? Choosing 3 people for a committee is a combination (positions are equal). Arranging 3 people in 3 ranked roles is a permutation (order determines who gets each role). Getting this distinction right is the first and most important step in solving every P and C problem.

Core Formulas

n factorial equals n times n minus 1 times n minus 2, continuing down to 1. nPr equals n factorial divided by n minus r factorial. nCr equals n factorial divided by r factorial times n minus r factorial. The symmetry property: nCr equals nC of n minus r. For circular arrangements of n distinct items, the count is n minus 1 factorial. For words with repeated letters, divide n factorial by the factorial of each repeated letter count.

Solved Example

In how many ways can 4 boys and 3 girls sit in a row with all girls together? Treat the 3 girls as one block. Arrange 5 entities (4 boys plus 1 block) in 5 factorial equals 120 ways. The girls within the block arrange in 3 factorial equals 6 ways. Total equals 120 times 6, which is 720 ways.

Interview Tips

Placement-level P and C questions rarely exceed two-step problems. For at least questions, always use complementary counting: Total minus arrangements with none of the required items. This eliminates the need to enumerate multiple individual cases and is the fastest approach for at-least type problems in every placement aptitude test.