__Multinomial Theorem and Example__The multinomial coefficient n1, n2, n3, ..., nk is used to denote the number of possible partitions of objects into groups having numerosity . The coefficient takes its name from the following multinomial expansion:

such that : n1 + n2 + ... + nk = n

**Example**

**In the game of bridge the entire deck of 52 cards is dealt out to 4 players.**

**What is the probability that**

a. one of the player receives all 13 spades;

b. each player receives 1 ace?

Answer

2.

**The number of possible ways to subdivide six objects into three groups of two objects each is given by the multinomial coefficient.**

Answer

3.

**How many methods that can be used for 12 students in 2 rooms,**so that the first room include 4 students in first room and 8 students in secondroom? Answer

There's C (12:4) how to choost from 12students to be place in the first room and there are see (12-4:8) how to select 8 students from 12-4=8 student left.