IB Mathematics · Grade 9 0 / 20
Combinatorics & Probability

Master the Art
of Counting

20 carefully crafted problems covering factorial, permutation, combination, and probability — designed to challenge and build deep understanding.

0 Correct
0 Wrong
20 Remaining
Accuracy

⚡ Quick Memory Points

Factorial
COUNTDOWN
Multiply all integers down to 1. Zero factorial = 1 (by definition).
n! = n×(n−1)×…×1
Permutation
ORDER MATTERS
Arranging r items from n where sequence changes the result.
P(n,r) = n!/(n−r)!
Combination
ORDER IGNORED
Selecting r items from n where order doesn't matter.
C(n,r) = n!/(r!(n−r)!)
Key Trick
DIVIDE BY r!
Combination = Permutation ÷ r! (removing duplicate orderings)
C = P ÷ r!
Probability
FAVORABLE/TOTAL
Always: 0 ≤ P ≤ 1. Complement rule: P(A') = 1 − P(A)
P = favorable/total
Trap Alert
WITH/WITHOUT
"With replacement" vs "without replacement" changes everything!
Watch the wording!