석 or 서 is a colloquial form of "세" like wise, 넉 or 너 is a colloquial form of "네" According to th Korean language standardization: Before the unit of "돈, 말, 발, 푼", 서 have to be used. Before the unit of "냥, 되, 섬, 자", 석 have to be used. The other cases, both 석 and 세 can be used. 서 돈(O) 세 돈(X) 석 냥(O) 세 냥(X) 석 잔(O) 세 잔(O) 석 달(O) 세 달(O)

Hello :) I think this is very interesting question but a little bit hard to understand because I guess this is related to Chinese character. You know, Korean usually use both 'Hangul' and 'Chinese character'. In this case, Chinese character is used this sentence. '석' is originated from Chinese character "三 (석 삼)" which have same meaning with 3. In short, the meaning is same between 석 and 삼. But when we say about period, we usually could say 석 instead of 삼. "석달(three months) is concept of period. And this concept could adapt other case as well. For example, when you say "4달(four months)", you would say "네달" or "넉달" not "사달". I'm not sure whether or not my explaining is helpful. Probably other people would explain more clearly than me. haha

Humm! Interesting question!