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

## Factorial notation

editA 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.