Rule of division (combinatorics)
In combinatorics, the rule of division is a counting principle. It states that there are ways to do a task if it can be done using a procedure that can be carried out in ways, and for each way, exactly of the ways correspond to the way.
In a nutshell, the division rule is a common way to ignore "unimportant" differences when counting things.
Applied to Sets
In the terms of a set: "If the finite set is the union of n pairwise disjoint subsets each with elements, then."As a function
The rule of division formulated in terms of functions: "If is a function from to where and are finite sets, and that for every value there are exactly values such that, then."Examples
Example 1- How many different ways are there to seat four people around a circular table, where two seatings are considered the same when each person has the same left neighbor and the same right neighbor?
Example 2
- We have 6 coloured bricks in total, 4 of them are red and 2 are white, in how many ways can we arrange them?