Revise: Permutation and Combination

Multiply the number of choices at each independent stage.

4×6×3 = 72 meal combos.

n! = n×(n−1)×...×2×1; 0!=1.

6! = 720.

P(n,n) = n!.

5 books → 120 orders.

P(n,r) = n!/(n−r)!.

P(8,3) = 336.

n!/(n₁!n₂!...) for repeated items.

LEVEL → 30 arrangements.

(n−1)! for circular arrangements.

6 people around a table → 120.

C(n,r) = n!/[r!(n−r)!].

C(8,3) = 56.

P(n,r) = C(n,r) × r!.

C(7,3)=35 → P(7,3)=210.

Probability = favorable/total, both via combinations.

5 red, 3 blue → P(both red)=5/14.

Always multiply, never add, independent choices.

26×10 = 260 passwords.

n! counts arrangements of n distinct objects in a row.

5!/3! = 20.

A special case of P(n,r) with r=n.

4 trophies → 24 orders.

Use when order matters among the chosen objects.

P(10,2) = 90.

Corrects overcounting from identical objects.

BANANA → 60 arrangements.

Fixing one seat removes rotational duplication.

5 people around a table → 24.

Use when order does NOT matter.

C(6,2) = 15.

r! accounts for orderings within each selected group.

C(9,2)=36 → P(9,2)=72.

Use the SAME counting method for numerator and denominator.

4 red, 6 blue → C(6,2)=15 ways to choose 2 blue.