If the object selected is not returned to the population before the next
object is selected, then an object can appear in the selected subset no more
than once. There are *n* choices in the population to fill the first
position, but then that leaves *n-1* choices in the population to fill
the second position. Therefore, there are ways to fill the first two
positions. Continuing this argument, we can see that there are
ways to select *k* objects without replacement
from a population of *n* objects when selection order is
distinguished. This number is commonly expressed using factorial notation,

2017-11-16