In how many ways can 3 people be seated in a row containing 7 seats?

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Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{Suppose} \mathrm{we} \mathrm{have} \mathrm{three} \mathrm{persons} \mathrm{A}, \mathrm{B} \mathrm{and} \mathrm{C}. \\ \mathrm{There} \mathrm{are} 7 \mathrm{seats}, \mathrm{hence} \\ \mathrm{Person} \mathrm{A} \mathrm{has} 7 \mathrm{options} \\ \mathrm{Person} \mathrm{B} \mathrm{has} 6 \mathrm{options} \left(\mathrm{As} \mathrm{one} \mathrm{seat} \mathrm{is} \mathrm{occupied} \mathrm{by} \mathrm{A}\right) \\ \mathrm{Similarly} \\ \mathrm{Person} \mathrm{C} \mathrm{has} 5 \mathrm{options}. \\ \mathrm{Hence}: \\ \mathrm{Total} \mathrm{number} \mathrm{of} \mathrm{ways}=7\times 6\times 5=\mathbf{210}\mathbf{ }\left(\mathbf{Answer}\right) \end{gathered}$$

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