Factorial notation

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.