Permutations & Combinations

Permutations and Combinations form the foundation of counting-based problems in aptitude tests and competitive exams. Permutation (nPr) deals with arrangements where order matters — how many ways can you arrange n items taking r at a time. Combination (nCr) handles selections where order does not matter — how many ways can you choose r items from n. Core concepts tested include factorial notation, arrangement of letters in words (with and without repetition), circular permutations, committee selection, and handshake problems. The key skill is recognizing whether a problem is about arrangements (use permutations) or selections (use combinations). Below are solved permutations and combinations questions covering all major exam patterns.

Key Takeaways

• Permutations = order matters (arranging). Combinations = order doesn't matter (selecting).
• nPr = n!/(n-r)!. nCr = n!/(r!×(n-r)!). Use nCr = nC(n-r) to simplify calculations.
• For arrangement of letters with repetition: reduce by dividing by (repeat_count)! for each repeated letter.

Frequently Asked Questions