Combinations with replacement In a factory there are 40 employees. A union of 5 people is being chosen. How many combinations are there for a union, if the union contains of 5 different roles, and each employee can hold more than one role (up to 5).
Thank you !

I am assuming that each role can be assigned to one person, though any one person may have more than one role.
There are $\binom{40}{5}$ ways to choose five members of the union.  Since there are five roles to assign, and each role can be assigned to one of $5$ union members, there are $5^5$ ways that the five roles can be assigned to the five chosen union members.
Using the product rule, that gives us $$\binom{40}{5} \cdot 5^5 = \frac{40!}{5!\,35!\,}\cdot 5^5 = \frac{40\cdot 39 \cdot 38\cdot 37 \cdot 36}{24}\cdot 5^4$$ totals ways this task can be accomplished. You can ease the computation by doing some nice cancellations.
