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
1. 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.
