Michael is a manager for his company, which covers multiple regions of the country.

(a) In region 1, there are 5 unique office buildings to which he would like to assign 10 indis- tinguishable senior workers and 40 indistinguishable entry-level workers. How many ways are there to assign workers to office buildings, such that each office has at least 1 senior worker and 4 entry-level workers?

(b) After some time, region 1 is idle (no jobs) and is looking to steal employees from the 7 other distinguishable regions. Suppose that all 7 other regions are overworked, each having a large number of indistinguishable senior employees. How many ways can region 1 take exactly 23 senior workers from the other regions, such that there are at least 3 regions from which 6 or more senior employees are taken?