For certain cases, we are asked to find permutations of items where some items are repeated.
- Same letters in string
- Dividing entities into groups
The number of permutations of a set n containing a identical object of one kind, b identical objects of another kind, c identical objects of another kind and so on,
Examples
Example 1
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 2
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