Permutation and Combination: Mixed P and C Problems

Concept Explanation

Mixed P and C problems combine permutations, combinations, circular arrangements, and restrictions in multi-step placement scenarios.

Key Formulas

• nPr = n!/(n − r)!, nCr = n!/(r!(n − r)!)
• Circular: (n − 1)!; identical items: n!/(p!q!)
• Break problem into stages and multiply independent counts

Example

Choose 3 from 8, then arrange chosen 3 in a row: 8C3 × 3! = 8P3 = 336.

Common Trap

Decide at each step whether order matters before choosing nPr or nCr.