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