When objects are distinct
When objects are distinct, i.e. differentiation can be made between objects while making selection, then the following cases arises.
I. Number of permutations of n things taken all at a time when things are not all different.
Out of n things,
p are exactly alike of one kind
q are exactly alike of second kind
r are exactly alike of third kind
and the remaining things are discrete or dissimilar.
Then the number of permutations of n things taken all at a time is
II The number of ways in which a Selection of One or More (i.e. at least one) objects can be made from n Distinct Objects is
III The number of ways in which a selection of none, one or more objects can be made from n Distinct Objects is