This case occurs when we wish to select *k* objects with replacement
from a population of *n* objects and selection order is distinguished.
Replacement implies that the same object could be selected multiple times. What
is required is to count the number of distinct sets of *k* objects could
be selected in this way. We can view this selection process by considering
the ways in which each of the positions, , of the set are filled.
Note that there are *n* choices in the population to fill the first
position, and since the object selected for this first position is then
returned to the population, there are *n* choices available for the
second selection as well. Therefore, there are ways to fill the first two
positions. Continuing this argument, we can see that there are ways to
select *k* objects with replacement from a population of *n*
distinguishable objects.

2017-02-15