Investigate!
  1. The Stanley Cup is decided in a best of 7 tournament between two teams. In how many ways can your team win? Let's answer this question two ways:

    1. How many of the 7 games does your team need to win? How many ways can this happen?

    2. What if the tournament goes all 7 games? So you win the last game. How many ways can the first 6 games go down?

    3. What if the tournament goes just 6 games? How many ways can this happen? What about 5 games? 4 games?

    4. What are the two different ways to compute the number of ways your team can win? Write down an equation involving binomial coefficients (that is, \({n \choose k}\)'s). What pattern in Pascal's triangle is this an example of?

  2. Generalize. What if the rules changed and you played a best of \(9\) tournament (5 wins required)? What if you played an \(n\) game tournament with \(k\) wins required to be named champion?

in-context