Calculate permutations (nPr) and combinations (nCr) with detailed step-by-step solutions and factorial calculations
Check if the same item can be selected multiple times
P(n,r) = C(n,r) × r!
C(n,r) = C(n,n-r)
P(n,n) = n!
C(n,0) = C(n,n) = 1
Permutation:
Race positions, passwords, arrangements
Combination:
Team selection, lottery numbers, committees
Permutations count arrangements where order matters (like race positions: 1st, 2nd, 3rd are different). Combinations count selections where order doesn't matter (like choosing team members: selecting A,B,C is the same as C,A,B). Permutations are always ≥ combinations for the same n and r.