Common Mistakes
Traps in Permutations & Combinations
5 mistake patterns students fall for. Each one shows the wrong approach vs the correct approach.
Confusing permutation and combination
FORMULAUsing nPr when order doesn't matter or nCr when it does.
✗ WRONG: Selecting a committee of 3 from 10: 10P3 = 720
✓ RIGHT: Selection (no order): 10C3 = 120. Use nPr only when arrangement matters.
Overcounting in distribution
FORMULANot dividing by k! when distributing into identical groups of equal size.
✗ WRONG: Split 6 people into 2 groups of 3: C(6,3) = 20
✓ RIGHT: C(6,3)/2! = 10 (groups are identical, so {A,B,C}/{D,E,F} = {D,E,F}/{A,B,C})
Forgetting the leading zero constraint
CASE MISSWhen forming n-digit numbers, the first digit cannot be 0.
✗ WRONG: 4-digit numbers from {0,1,2,3}: 4! = 24
✓ RIGHT: First digit: 3 choices (not 0). Remaining: 3! = 6. Total: 3*6 = 18.
Missing cases in constrained counting
CASE MISSNot considering all valid partitions or configurations.
✗ WRONG: Only considering one way to split when multiple distributions are possible
✓ RIGHT: List all valid partitions/cases systematically, then count each.
Circular vs linear arrangement
FORMULAUsing n! instead of (n-1)! for circular arrangements.
✗ WRONG: 8 people around a circular table: 8! ways
✓ RIGHT: Fix one person, arrange the rest: 7! = 5040 ways