The binomial is a special case of the more general multinomial distribution:

where p₁ + . . . + p_k = 1 and n₁ + . . . . + n_k = n. Each observation of a random variable has k possible outcomes, with probabilities p₁, . . ., p_k, and the observed total numbers of each possible outcome after n independent observations are made are respectively n₁, . . . . , n_k. Suppose that 60% of calls to a telephone banking enquiry service are for account balance requests, 20% are for payment confirmations, 10% are for transfer requests and 10% are to open new accounts. Find the probability that out of twenty calls to this service there will be ten balance requests, five payment confirmations, three transfers and two new accounts.

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P(n,..., n): = n! m!... n! (P)" ... (Pr)"