1. Fundamental Counting Principle
If one event has m outcomes and another has n outcomes, the total number of outcomes for both events is:
Total = m × n × ···
Example
3 shirts × 4 pants =
12 outfits
2. Permutation — Order Matters
P(n,r) = n! / (n−r)!
n = total items
r = items chosen
Order MATTERS
Example: arrange 3 from {A,B,C,D,E}
P(5,3) = 5×4×3 =
60
3. Combination — Order Does NOT Matter
C(n,r) = n! / [r! × (n−r)!]
Also written as nCr or C(n,r)
Key: C(n,r) = C(n, n−r)
Example: choose 3 from {A,B,C,D,E}
C(5,3) = 5!/(3!×2!) = 120/12 =
10
4. Basic Probability
P(A) = (favorable outcomes) / (total outcomes)
0 ≤ P(A) ≤ 1
P(A) + P(A') = 1 [complement rule]
5. Addition Rule
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
Mutually exclusive: P(A ∪ B) = P(A) + P(B)
6. Multiplication Rule
Independent events:
P(A ∩ B) = P(A) × P(B)
Dependent events:
P(A ∩ B) = P(A) × P(B|A)
7. Conditional Probability
P(B|A) = P(A ∩ B) / P(A)
Example
P(A)=0.4, P(A∩B)=0.12 ⟹ P(B|A) = 0.12/0.4 =
0.3
⚡ Must-Memorize Quick Facts