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Suppose you are the coach of a team with n players. Among those players, k players...

Suppose you are the coach of a team with n players. Among those players, k players can be in the starting line-up. One of the players in the starting line-up can be the captain of the team.

(a) Answer the question “How many ways can you choose a starting line-up and a captain?” in two different ways. Make sure to explain your reasoning. Hint: Choose the starting line-up and captain in two different orders.

(b) Use your work from above to make a combinatorial identity. Explain your reasoning

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