distributing z different objects among k people almost evenly We have z objects (all different), and we want to distribute them among k people ( k < = z ) so that the distribution is almost even.
i.e. the difference between the number of articles given to the person with maximum articles, and the one with minimum articles is at most 1.
We need to find the total number of ways in which this can be done
for example if there are 5 objects and 3 people the number of such ways should be 90.
I am not sure how we get this value.

Each person will get either $\lfloor \frac{z}{k}\rfloor$ or $\lceil \frac{z}{k}\rceil$ objects.  These are the floor and ceiling functions.
