Counting Principles

This page deals with all the counting principles in the HL course: Arrangements, Permutations and Combinations. You need to be familiar with combinations for the Binomial Theorem, but it is also useful in its own right to be able to work out, for example, how many ways there are of getting a hand of blackjack in a card game or finding how many different tickets are possible in a lottery. There is always more than one way of solving a problem. This page will enable to be confident in several methods, in order that you can have a flexible problem-solving strategy.


Key Concepts

On this page, you should learn to count

  • Arrangements
  • Permutations
  • Combinations

Summary

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Test Yourself

Try this quiz to practise questions about arrangements


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Try this quiz to practise questions about combinations and permutations


START QUIZ!

Exam-style Questions

Question 1

A team of five players is chosen from six males and 5 females.

  1. Determine how many different teams can be formed.
  2. Determine how many different teams can be formed consisting of 3 males and 2 females.
  3. Determine how many different teams can be formed if the team consists of more females than males

Hint

Full Solution

Question 2

A five-digit number is formed by using the digits 1-5 exactly once.

  1. How many five-digit numbers are there?
  2. How many of these five-digit numbers are even?

Hint

Full Solution

Question 3

Seven students are placed at random in a line.

  1. How many different arrangements are there?
  2. What is the probability that the two youngest students are separated?

Hint

Full Solution

MY PROGRESS

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