Posted by **Genie_math** on Wednesday, October 3, 2012 at 9:01pm.

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) ??

- Discrete math -
**Reiny**, Wednesday, October 3, 2012 at 9:17pm
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.)

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