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

AQA AS Maths 2017 | Pure Maths | Binomial Expansion | Binomial Expansion | - |

AQA AS/A2 Maths 2017 | Pure Maths | Binomial Expansion | Binomial Expansion | - |

CBSE XI (India) | Algebra | Binomial Theorem | Pascal's triangle | - |

Edexcel AS Maths 2017 | Pure Maths | Binomial Expansion | Binomial Expansion | - |

Edexcel AS/A2 Maths 2017 | Pure Maths | Binomial Expansion | Binomial Expansion | - |

OCR AS Maths 2017 | Pure Maths | Binomial Expansion | Binomial Expansion | - |

OCR MEI AS Maths 2017 | Pure Maths | Binomial Expansion | Binomial Expansion | - |

Universal (all site questions) | B | Binomial Theorem | Pascal's triangle | - |