Question

There are 12 European cities that Dan would eventually like to visit. On his next vacation,though, he only has time to visit 3 of the cities: one on Monday, one on Tuesday, and one onWednesday. He is now trying to make a schedule of which city he'll visit on which day. How manydifferent schedules are possible? (Assume that he will not visit a city more than once.)

Answer 1

$\begin{gathered} 12\text{ cities} \\ 3\text{ cities} \\ \text{Monday he can visit 12 cities} \\ \text{Tuesday he can visit 11 cities} \\ \text{Wednesday he can visit 10 cities} \\ \text{Different schedules= 12}\cdot11\cdot10 \\ \text{Different schedules= 1,320} \end{gathered}$