Permutation & Combination Calculator | nPr & nCr Solver
Calculate permutations (nPr) and combinations (nCr) with or without repetitions. Get step-by-step factorial simplifications and circular permutations using this free permutation combination calculator.
Total Arrangement Combinations
120
Solved
Alternate Counting Perspectives
Complement nCn-r120
Total Factorial (n!)3628800
Pascal's Triangle Alignment Map (Row n = 10)
10C01
10C110
10C245
10C3120
10C4210
10C5252
10C6210
10C7120
10C845
10C910
10C101
Pascal row highlighted bubble matches combinations select parameter index (r = 3).
Factorial Cancellation Steps
Combinations without repetition formula: nCr = n! / (r! * (n - r)!)
10C3 = 10! / (3! * 7!)
Simplified top & bottom cancellation: (10 × 9 × 8) / (1 × 2 × 3)
Solved Value = 120