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Question

# a. In how many ways can a club with 20 members choose a president and a vice president?b. In how many ways can the club choose a 2-person governing council?

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a) Since the order (or positions) matter, then permutation is used. With two positions to fill up, then the 20 members can be arranged in:

\begin{align*} _{20}P_2 &= \dfrac{20!}{(20-2)!} \\ &= \dfrac{20 \cdot 19 \cdot \cancel{18!}}{ \cancel{18!} } \\ &= 380 \text{ ways}. \\ \end{align*}

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