Question

In a high school band there are 11 students in the drumline section. The drumline for a football game consists of 6 students. In how many ways can the drumline be formed for a football game?

Answer 1

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:

$C_{11}^6= \frac{11!}{6!\cdot (11-6)!}= \frac{1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9\cdot10\cdot11}{1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot1\cdot2\cdot3\cdot4\cdot5} = \frac{7\cdot8\cdot9\cdot10\cdot11}{2\cdot3\cdot4\cdot5} =462$.

Answer: 462 ways to complete the drumline for a football game.