- #1

master cherundo

- 14

- 0

## Homework Statement

Suppose that a basketball league has 32 teams, split into two conferences of 16 teams each. Each conference is split into three divisions. Suppose that the North Central Division has five teams. Each of the teams in the North Central Division plays four games agains each of the other teams in this division, three games against each of the 11 remaining teams in the conference, and two games against each of the 16 teams in the other conference. In how many different orders can the games of one of the teams in the North Central DIvision be scheduled?

## Homework Equations

[tex]\frac{n!}{n_1n_2 \cdots n_k}[/tex]

## The Attempt at a Solution

Well, I think it would be [tex]\frac{81!}{4!^4 \times 11!^3 \times 16!^2}[/tex]

But, it is a hard stuff to compute this if we do not use calculator. And, I believe it has implementation with how to distribute [tex]82[/tex] objects into [tex]n[/tex] boxes. Unfortunately, I do not know how to find [tex]n[/tex].