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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. You can get a better display of the maths by downloading special TeX fonts from jsMath. In the meantime, we will do the best we can with the fonts you have, but it may not be pretty and some equations may not be rendered correctly.

## 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.

Full Glossary List

## This question appears in the following syllabi:

SyllabusModuleSectionTopicExam Year
AQA A-Level (UK - Pre-2017)S1The Binomial DistributionCombinations-
AQA AS Maths 2017Pure MathsBinomial ExpansionPermutations and Combinations-
AQA AS/A2 Maths 2017Pure MathsBinomial ExpansionPermutations and Combinations-
CBSE XI (India)AlgebraPermutation and CombinationsFactorial-
CCEA A-Level (NI)S1The Binomial DistributionCombinations-
CIE A-Level (UK)S1The Binomial DistributionCombinations-
Edexcel A-Level (UK - Pre-2017)S2The Binomial DistributionCombinations-
Edexcel AS Maths 2017StatisticsStatistical DistributionsPermutations and Combinations-
Edexcel AS/A2 Maths 2017StatisticsStatistical DistributionsPermutations and Combinations-
I.B. Higher Level7The Binomial DistributionCombinations-
Methods (UK)M15The Binomial DistributionCombinations-
OCR A-Level (UK - Pre-2017)S1The Binomial DistributionCombinations-
OCR AS Maths 2017StatisticsDiscrete and Binomial DistributionsPermutations and Combinations-
OCR MEI AS Maths 2017StatisticsThe Binomial DistributionPermutations and Combinations-
OCR-MEI A-Level (UK - Pre-2017)S1The Binomial DistributionCombinations-
Pre-U A-Level (UK)ProbThe Binomial DistributionCombinations-
Universal (all site questions)BThe Binomial DistributionCombinations-
WJEC A-Level (Wales)S1The Binomial DistributionCombinations-