Worked problem pages
Each page explains the idea, then works through real problems from the Mathyessy bank step by step.
Permutations practice problemsPermutations count arrangements where order matters: lineups, rankings, codes and seatings.Combinations practice problemsCombinations count selections where order does not matter: committees, teams, toppings and hands of cards.Probability practice problemsProbability is counting twice: once for the outcomes you want and once for all possible outcomes.Complementary counting practiceWhen the cases you want are messy, count the ones you don't want and subtract.Casework counting practiceBreak a hard count into a few easy ones. The key is choosing cases that don't overlap and don't miss anything.Expected value practice problemsExpected value is the long-run average: what a game pays per play if you played it many, many times.Stars and bars practice problemsHow many ways can you share identical candies among kids? Stars and bars turns it into a single combination.Pigeonhole principle practice'How many must you pick to guarantee…?' Imagine the unluckiest possible picks, then add one.Grid path counting practiceA shortest path on a grid is just a word made of R's and U's. Counting paths means counting those words.
Every Counting & Probability practice set in Mathyessy
Each link opens that topic's question set in the free app. Questions get harder as you go, and you get instant feedback after each answer.
- Multiplication Principle
- Addition Principle
- Factorials
- Permutations · worked problems
- Combinations · worked problems
- Probability Basics · worked problems
- Coin And Dice Probability
- Marble Probability
- Complementary Counting · worked problems
- Casework Counting · worked problems
- Expected Value · worked problems
- Pascals Triangle
- Stars And Bars · worked problems
- Recursion
- Pigeonhole Principle · worked problems
- Independent And Dependent Events
- Passwords And Codes
- Grid Paths · worked problems
- Venn Diagrams
- Odds