In how many ways can you arrange the five numbers 1, 2, 3, 4, 5?

Think about the number of choices: five for the first choice, four for the second, and so on, so the number of ways is:

5 \times 4 \times 3 \times 2 \times 1 = 120

This calculation is called 5 factorial and is written 5!

In general for any positive integer n , n! = n(n-1)(n-2)... 1 \quad and 0! = 1.

Think about the number of choices: five for the first choice, four for the second, and so on, so the number of ways is:

5 \times 4 \times 3 \times 2 \times 1 = 120

This calculation is called 5 factorial and is written 5!

In general for any positive integer n , n! = n(n-1)(n-2)... 1 \quad and 0! = 1.

## Software/Applets used on this page

## Glossary

### factorial

n! = n(n-1)(n-2)(n-3)...3.2.1.

### integer

a positive or negative whole number.

### union

The union of two sets A and B is the set containing all the elements of A and B.

## This question appears in the following syllabi:

Syllabus | Module | Section | Topic | Exam Year |
---|---|---|---|---|

AP Calculus AB (USA) | 4 | Integration | Observation | - |

AP Calculus BC (USA) | 4 | Integration | Observation | - |

AQA A-Level (UK - Pre-2017) | C3 | Integration | Observation | - |

AQA A2 Maths 2017 | Pure Maths | Integration | Reverse Chain Rule | - |

AQA AS/A2 Maths 2017 | Pure Maths | Integration | Reverse Chain Rule | - |

CCEA A-Level (NI) | C4 | Integration | Observation | - |

CIE A-Level (UK) | P2 | Integration | Observation | - |

Edexcel A-Level (UK - Pre-2017) | C4 | Integration | Observation | - |

Edexcel A2 Maths 2017 | Pure Maths | Integration | Reverse Chain Rule | - |

Edexcel AS/A2 Maths 2017 | Pure Maths | Integration | Reverse Chain Rule | - |

I.B. Higher Level | 6 | Integration | Observation | - |

I.B. Standard Level | 6 | Integration | Observation | - |

Methods (UK) | M9 | Integration | Observation | - |

OCR A-Level (UK - Pre-2017) | C4 | Integration | Observation | - |

OCR A2 Maths 2017 | Pure Maths | Integration Techniques | Reverse Chain Rule | - |

OCR MEI A2 Maths 2017 | Pure Maths | Integration Techniques | Reverse Chain Rule | - |

OCR-MEI A-Level (UK - Pre-2017) | C3 | Integration | Observation | - |

Pre-U A-Level (UK) | 5 | Integration | Observation | - |

Scottish Advanced Highers | M1 | Integration | Observation | - |

Scottish (Highers + Advanced) | HM3 | Integration | Observation | - |

Scottish Highers | M3 | Integration | Observation | - |

Universal (all site questions) | I | Integration | Observation | - |

WJEC A-Level (Wales) | C4 | Integration | Observation | - |