Exam Practice
Probability &
Combinations
20 exam-style multiple choice questions
with full explanations
Questions
20 MCQ
Time Limit
40 min
Topics
7 Types
Difficulty
★★★☆☆
📚 Core Concepts
Probability & Combinations
Key Formulas to Memorise
Combination C(n,r)
C(n,r) = n! / [r!(n-r)!]
→ Choosing r items from n, ORDER does NOT matter
Permutation P(n,r)
P(n,r) = n! / (n-r)!
→ Arranging r items from n, ORDER DOES matter
Basic Probability
P(A) = (# favourable outcomes) / (# total outcomes)
→ Always between 0 and 1 (inclusive)
Addition Rule
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
→ If mutually exclusive: P(A ∪ B) = P(A) + P(B)
Multiplication Rule
P(A ∩ B) = P(A) · P(B|A)
→ If independent: P(A ∩ B) = P(A) · P(B)
Binomial Probability
P(X=k) = C(n,k) · p^k · (1-p)^(n-k)
→ n trials, probability p each, exactly k successes
Quick Reference
C(n,0) = C(n,n) = 1
Always 1
Choosing none or all
C(n,r) = C(n,n-r)
Symmetry
C(10,3) = C(10,7)
P(A') = 1 − P(A)
Complement
Use when "at least" appears
P(n,r) = C(n,r) · r!
Perm = Comb × r!
Order multiplier
Worked Examples
Example 1 — Basic Combination
How many ways can a committee of 3 be chosen from 7 people?
C(7,3) = 7! / (3! × 4!)
= (7 × 6 × 5) / (3 × 2 × 1) = 210 / 6
= 35 ways
Example 2 — Probability with Combinations
A bag has 4 red and 6 blue balls. Two are drawn at random. P(both red)?
Total ways = C(10,2) = 45
Favourable (2 red from 4) = C(4,2) = 6
P = 6/45 = 2/15
Example 3 — Complement Method
P(at least one head in 3 coin flips)?
P(no heads) = (1/2)³ = 1/8
P(at least one) = 1 − 1/8
= 7/8
Final Score
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