A notation used to divide combinations into smaller sub-boxes.

Notation

Where:

Example

Example 1

Split a group of 12 people into 3 groups of 2 people, 5 people and 5 people

Soln

With the corresponding to repeated groups

Example 2

For example, if we were asked for the permutations of the word: ROOM then we would encounter there are 2 O’s A word does not care about the type of O given, so an O in the second place is the same as an O in the first. The total permutations of ROOM is 12. Not 24 We use Box Occupant Based Thinking And clump the 2 O as the same thing. total permutations /# of times it is repeated 4! / 2! = 12

Example 3

How many arrangements of the word bookkeeper is there? 10 characters all together 2 o’s 2 k’s 3 e’s 10!/(2!2!3!) = 151200