其它
Mary, Nancy, and Peter are playing archery. They have $$7$$ identical arrows in total. Each of them must shoot at least once. How many different ways can they shoot the arrows? 
Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration
There are 3 different people here, so order does matter. Each of them must shoot at least once:  $$7=1+1+5$$  $$7=1+2+4$$  $$7=1+3+3$$  $$7=1+4+2$$  $$7=1+5+1$$  $\textasciitilde$  $$7=2+1+4$$  $$7=2+2+3$$  $$7=2+3+2$$  $$7=2+4+1$$  $\cdots$  And so on. If we keep listing, total will be:  $$5+4+3+2+1=15$$ ways 