Multinomial Distribution

Below is the multinomial formula used in multinomial distribution in statistics (probabilidad multinomial). To explain what a multinomial distribution or multinomial probability distribution is, let's suppose there are n objects. We put the n objects into boxes with each box having k objects. Simple math shows that we need n/k boxes.

Multinomial formula used in multinomial distribution problems

What is the multinomial formula?

The multinomial formula shown above is the number of ways to split the objects (n objects) up into boxes. The multinomial formula assumes that it makes a difference what box each group is put into.

The general form of Multinomial formula

 In general the multinomial formula says that if you are putting n objects in m groups with k₁ objects in the first group, k₂ objects in the second, etc... and k_m objects in group m, then there are:

ways of doing this. Bear in mind that:

Relationship between multinomial formula and combinations formula

When m = 2, the multinomial formula becomes the same as the combinations formula.