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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.

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## 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:

SyllabusModuleSectionTopic
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
N Statistics - DistributionsN1 Discrete Probability DistributionsPermutations and Combinations
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