Next: Some more identities
Up: Selection and Binomial Coefficients
Previous: Selection and Binomial Coefficients
Contents
The number of ways of choosing objects out of objects is

ordered 
unordered 
no repeats 


repeats 


The only entry that needs justification is
. But there
is a onetoone correspondance betwen the set of ways of choosing out
of unordered with possible repeats and the set of all binary strings
of length with zeros and ones. For suppose there
are occurences of element , . Then
There are
such strings (choosing where to put the 's).
root
20020610