Examples

Multinomial: Soft drinks preferred

Folks coming to a party prefer Coke (55%), Pepsi (25%), or Dew (20%). If 20 people order drinks in sequence, what is the probability that exactly 12 have Coke and 5 have Pepsi and 3 have Dew?

Solution

The multinomial coefficient gives the number of ways to assign 20 people into bins according to preferences matching the given numbers, and and .

Each such assignment is one sequence of outcomes. All such sequences have probability .

The answer is therefore: