There are eighteen guard posts. How many ways can 25 not indistinguishable (That is, they are distinguishable.)guards be distributed to the guard posts, so that no post is empty?
Try - (25 choose 18) ??
Think of it this way:
Every time all the 18 posts are filled, there will be a set of 7 guards left out.
So the question becomes, how many set of 7 from 25 can we find, which is
C(25,7) or C(25,8) , both yield the same answer.
BTW, your clarification in brackets is a contradiction
you probably meant to say
((That is, they are NOT distinguishable.)