[tex]e.g\\a\ small\ class\ has\ 15\ students\ and\ we\ will\ choose\ 3-person\ team\\\\the\ number\ of\ possible\ teams\ is\\\\ {n \choose k}={15 \choose 3}= \frac{15!}{3!\cdot(15-3)!}= \frac{12!\cdot13\cdot14\cdot15}{2\cdot3\cdot12!} = \frac{13\cdot2\cdot7\cdot3\cdot5}{2\cdot3} = 13\cdot7\cdot5=455[/tex]
