Probability & Combinatorics

Master the Art of
Counting & Chance

20 carefully crafted questions covering permutations, combinations, and probability — the ones students get wrong most.

Questions

Topics

Difficulty Levels

ORDER matters → nPr

Permutation: arranging in a line, passwords, races

ORDER doesn't → nCr

Combination: choosing a team, picking lottery numbers

P(A or B) = P(A)+P(B)−P(A∩B)

Don't double-count the overlap!

P(A and B) = P(A)×P(B|A)

Conditional: "given" = update denominator

Complement: 1 − P(none)

"At least one" → easier to find "none" first

nCr = nC(n−r)

Choosing 3 from 10 = leaving out 7 from 10

Key Formulas

Quick Reference

Permutation

\( P(n,r) = \dfrac{n!}{(n-r)!} \)

Combination

\( C(n,r) = \dfrac{n!}{r!(n-r)!} \)

Addition Rule

\( P(A \cup B) = P(A)+P(B)-P(A \cap B) \)

Multiplication Rule

\( P(A \cap B) = P(A) \cdot P(B|A) \)

Independent Events

\( P(A \cap B) = P(A) \cdot P(B) \)

Complement

\( P(A') = 1 - P(A) \)

0 of 20 answered

20 Problems