Can we apply the division rule to this problem :
On each of the 22 work days in a particular month, every employee of a start-up venture was sent a company communication. If a total of 4730 company communications were sent, how many employees does the company have, assuming that no staffing changes were made that month?
From the Discrete math book :
If the finite set A is the union of n pairwise disjoint subsets each with d elements, then n = |A|/d
Using this formula from the book, I calculated this to be 4730/22 = 215
Can you please confirm if this is correct and if my understanding is right, because the book mentions this to be a hard problem and I am not sure if I am missing something ?
Best Answer
I don't know how this is a discrete math or combinatorics problem. You can solve it without any of those tools. Think about it like this:
$$\text{Total Communications} = \text{Number of Employees} \times \text{Number of Days} $$
This suffices because the problem states that every employee receives the communication on every workday. So you can treat employees as one unit and the days as one unit, rather than needing to think about subsets of them.
A classic combinatorial problem would involve needing to tackle subsets of either employees or days.