multinomial distribution is a generalization of the binomial distribution. For n independent trials each of which leads to a success for exactly one of k categories, with each category having a given fixed success probability, the multinomial distribution gives the probability of any particular combination of numbers of successes for the various categories.
The binomial distribution is the probability distribution of the number of successes for one of just two categories in n independent Bernoulli trials, with the same probability of success on each trial. In a multinomial distribution, the analog of the Bernoulli distribution is the categorical distribution, where each trial results in exactly one of some fixed finite number k possible outcomes