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 |
---|---|---|---|

AQA A-Level (UK - Pre-2017) | S1 | The Binomial Distribution | Combinations |

AQA AS Maths 2017 | Pure Maths | Binomial Expansion | Permutations and Combinations |

AQA AS/A2 Maths 2017 | Pure Maths | Binomial Expansion | Permutations and Combinations |

CBSE XI (India) | Algebra | Permutation and Combinations | Factorial |

CCEA A-Level (NI) | S1 | The Binomial Distribution | Combinations |

CIE A-Level (UK) | S1 | The Binomial Distribution | Combinations |

N Statistics - Distributions | N1 Discrete Probability Distributions | Permutations and Combinations | |

Edexcel A-Level (UK - Pre-2017) | S2 | The Binomial Distribution | Combinations |

Edexcel AS Maths 2017 | Statistics | Statistical Distributions | Permutations and Combinations |

Edexcel AS/A2 Maths 2017 | Statistics | Statistical Distributions | Permutations and Combinations |

I.B. Higher Level | 7 | The Binomial Distribution | Combinations |

Methods (UK) | M15 | The Binomial Distribution | Combinations |

OCR A-Level (UK - Pre-2017) | S1 | The Binomial Distribution | Combinations |

OCR AS Maths 2017 | Statistics | Discrete and Binomial Distributions | Permutations and Combinations |

OCR MEI AS Maths 2017 | Statistics | The Binomial Distribution | Permutations and Combinations |

OCR-MEI A-Level (UK - Pre-2017) | S1 | The Binomial Distribution | Combinations |

Pre-U A-Level (UK) | Prob | The Binomial Distribution | Combinations |

Universal (all site questions) | B | The Binomial Distribution | Combinations |

WJEC A-Level (Wales) | S1 | The Binomial Distribution | Combinations |