Assume a mid-size corporation is hiring 12 new software developers from among 20 prospective candidates. (Assume a candidate may only be hired for one position.) (a) Assuming the 12 openings are entirely unique, how many distinct ways can 10 candidates be hired from among the 20? (b) Assuming the 12 openings are exactly the same, and we only care about which of the 20 candidates are hired, how many ways can 12 candidates be selected from the original 20? (c) Assuming the 12 openings are organized into 3 distinct positions (ex: front-end developer, back-end developer), each of size 4, how many ways can the positions be filled? (d) Assuming the 12 openings are organized into 3 indistinct teams (where only the employees chosen per team matters) of size 4, how will the response to (c) change?