If the band consists of 11 students and you have to choose 6 students for the drumline for a football game, then you have to calculate the number of combinations:
[tex]C_{11}^6= \frac{11!}{6!\cdot (11-6)!}= \frac{1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9\cdot10\cdot11}{1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot1\cdot2\cdot3\cdot4\cdot5} = \frac{7\cdot8\cdot9\cdot10\cdot11}{2\cdot3\cdot4\cdot5} =462[/tex].
Answer: 462 ways to complete the drumline for a football game.
