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Five people are playing a game where they win if they are in a chair when the music stops. But there are only two chairs. How many different pairs of people are possible?

Answer :

[tex]\begin{gathered} Number\text{ of people}\Rightarrow5 \\ \text{Number of chair}\Rightarrow2 \\ The\text{ situatin to win the game is,} \\ 5_{C2}=\frac{5!}{3!2!} \\ 5_{C2}=\frac{5\times4\times3\times2\times1}{3\times2\times1\times2\times1} \\ 5_{C2}=10 \end{gathered}[/tex]

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