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  1. You must simply choose 6 friends from a group of 14. This can be done in \({14 \choose 6}\) ways. We can find this number either by using Pascal's triangle or the closed formula: \(\frac{14!}{8!\cdot 6!} = 3003\text{.}\)

  2. Here you must count all the ways you can permute 6 friends chosen from a group of 14. So the answer is \(P(14, 6)\text{,}\) which can be calculated as \(\frac{14!}{8!} = 2162160\text{.}\)

    Notice that we can think of this counting problem as a question about counting functions: how many injective functions are there from your set of 6 chairs to your set of 14 friends (the functions are injective because you can't have a single chair go to two of your friends).

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