A-level Mathematics/Edexcel/Statistics 2/The binomial and Poisson distributions

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Factorial notation[edit]

A factorial of a positive integer n is the product of all the natural numbers from 1 to n. The factorial of n is denoted by n! (n factorial). Factorials are used in probability distributions.

Factorials can be used to find the possible number of permutations or combinations of the elements of a set. For example, let S represent the set of beads in a bag. The bag has 2 blue and 2 green beads. The beads are taken out of the bag and arranged. The possible arrangements are:

  • BBGG
  • BGGB
  • BGBG
  • GBGB
  • GBBG
  • GGBB

where B represents a blue bead and G represents a green bead.

We can see that there are 8 possible arrangements. We can use factorials to work out the number of possible arrangements.